Question 1

The price of an article is reduced by 33%. By what percentage must the new reduced price be increased so that it returns exactly to the original price?

Accepted Answer

Introduction / Context:This question examines the reverse effect of a large percentage decrease and how much percentage increase is needed to get back to the original value. It is an important concept that a 33% decrease cannot be undone by a 33% increase. Understanding the correct relationship is very useful in questions involving discounts, salaries, and stock prices.Given Data / Assumptions:The original price of an article is P.The price is cut by 33%.We must find the percentage increase required on the reduced price to restore it to P.There are no further changes or additional charges involved.Concept / Approach:A decrease of d percent leaves (100 - d)% of the original value. To restore the original value from this reduced value, we need a percentage increase that solves the equation reduced * (1 + x/100) = original. There is also a direct formula: required percentage increase = (d / (100 - d)) * 100. We apply this formula with d = 33 to find the required increase. Calculating with a base of 100 units makes the logic easier to see.Step-by-Step Solution:Step 1: Assume the original price P is 100 units.Step 2: A decrease of 33% means the new price is 100 * (1 - 33/100) = 100 * 0.67 = 67 units.Step 3: Let the required percentage increase be x% on this reduced price.Step 4: To reach the original 100 units, we need 67 * (1 + x/100) = 100.Step 5: Rearrange: 1 + x/100 = 100 / 67.Step 6: Therefore x/100 = (100 / 67) - 1 = (100 - 67) / 67 = 33 / 67.Step 7: Multiply by 100: x = (33 / 67) * 100 ≈ 49.25 percent.Verification / Alternative check:Using the standard formula directly gives the same result. Required percentage increase = (d / (100 - d)) * 100, with d = 33. So x = (33 / (100 - 33)) * 100 = (33 / 67) * 100, which is approximately 49.25 percent. This agrees exactly with the step by step calculation with a base of 100 units, confirming that we need roughly a 49.25 percent increase to undo a 33 percent decrease.Why Other Options Are Wrong:33 percent would restore only 67 * 1.33 = 89.11 units, which does not reach the original 100 units.24.81 percent is too small and clearly will not recover the original 100 from 67.41.25 percent also falls short since 67 * 1.4125 is still less than 100.66 percent would overshoot the original amount considerably, taking 67 to over 110 units.Common Pitfalls:The most common mistake is to assume that the same percentage that was used for the decrease will restore the original value when used as an increase. This fails because the base amount for the increase is smaller after the reduction. Another pitfall is to misapply the formula by placing 100 in the wrong position of the fraction or forgetting to multiply by 100 at the end. To avoid such errors, always work with a hypothetical base value of 100 units and carefully track how the percentage changes affect it step by step.Final Answer:The reduced price must be increased by approximately 49.25 percent to restore the original price.

Question 2

Two numbers are 50% and 90% less than a certain third number. By what percentage must the smaller of these two numbers be increased so that it becomes equal to the larger number?

Accepted Answer

Introduction / Context:This question tests the ability to compare numbers that are given as percentage reductions from a common reference value. It then asks for the percentage increase required to move from the smaller number to the larger number. Such problems often appear in percentage and ratio sections of competitive examinations.Given Data / Assumptions:A third reference number, call it T, is given implicitly.The first number (larger among the two derived numbers) is 50% less than T.The second number (smaller one) is 90% less than T.We must find the percentage increase required to raise the smaller number to the larger number.Concept / Approach:If a number is 50% less than T, then it equals T * (1 - 50/100) = 0.5 * T. If another number is 90% less than T, it equals T * (1 - 90/100) = 0.1 * T. To find how much the smaller must increase to become the larger, we take the difference between the two and divide by the smaller, then convert that ratio into a percentage. The formula is required percent increase = (larger - smaller) / smaller * 100.Step-by-Step Solution:Step 1: Let the reference number be T.Step 2: The larger number, A, is 50% less than T, so A = T * (1 - 50/100) = 0.5 * T.Step 3: The smaller number, B, is 90% less than T, so B = T * (1 - 90/100) = 0.1 * T.Step 4: The increase needed to go from B to A is A - B = 0.5 * T - 0.1 * T = 0.4 * T.Step 5: Required percentage increase = (A - B) / B * 100 = (0.4 * T / 0.1 * T) * 100.Step 6: Simplify the fraction: 0.4 * T / 0.1 * T = 4, so the required percentage = 4 * 100 = 400 percent.Verification / Alternative check:We can also choose a convenient value for T, such as T = 100. Then A = 50% less than 100 = 50. B = 90% less than 100 = 10. The increase required to go from 10 to 50 is 40. So the percentage increase = (40 / 10) * 100 = 400 percent. This numerical example confirms the algebraic reasoning and gives exactly the same result.Why Other Options Are Wrong:80 percent would be the required increase if the smaller number were 25, increasing to 45, which is not the case here.40 percent would be correct if the smaller number were 100 and needed to move to 140, but that does not match the given relationships.44.44 percent is a common trap value from inverse percentage problems but not applicable in this scenario.60 percent is also another distractor that does not arise from the ratio between 50 and 10.Common Pitfalls:Students sometimes mistakenly subtract the percentage reductions (90% - 50% = 40%) and directly use that as the required increase, which is wrong because the increase must be measured relative to the smaller number, not relative to the reference number. Another pitfall is reversing the roles of the numerator and denominator when calculating the percent increase. Always remember that the percentage increase is based on the original smaller value as the reference. Using actual numbers after assigning a convenient value to T helps avoid these conceptual mistakes.Final Answer:The smaller number must be increased by 400 percent to become equal to the larger number.

Question 3

A student multiplies a number by 3/10 instead of multiplying it by 10/3. What is the percentage error in the student's result compared to the correct result?

Accepted Answer

Introduction / Context:This problem assesses understanding of percentage error when an incorrect multiplier is used instead of the correct one. It is a classic example from quantitative aptitude where a student uses the reciprocal of the intended factor, leading to a significant mistake. Calculating the relative error as a percentage is an essential skill in many exam and practical contexts.Given Data / Assumptions:Let the original number be N.The correct operation should be multiplication by 10/3.The student mistakenly multiplies the number by 3/10 instead.We must find the percentage error of the student's result relative to the correct result.Concept / Approach:First, compute the correct result, which is N * (10/3). Then compute the wrong result, which is N * (3/10). The absolute error is the difference between the correct result and the wrong result. The percentage error is given by (absolute error / correct result) * 100. We can treat N as a symbolic variable and simplify the ratio using algebra, so that N cancels out and we get a simple percentage.Step-by-Step Solution:Step 1: Correct result = N * (10/3).Step 2: Wrong result = N * (3/10).Step 3: Absolute error = correct result - wrong result = N * (10/3) - N * (3/10).Step 4: Factor out N: error = N * (10/3 - 3/10).Step 5: Compute the bracket: 10/3 - 3/10 = (100/30 - 9/30) = 91/30.Step 6: So error = N * (91/30).Step 7: Percentage error = (error / correct result) * 100.Step 8: Substitute: percentage error = [N * (91/30)] / [N * (10/3)] * 100.Step 9: Simplify the fraction: (91/30) / (10/3) = (91/30) * (3/10) = 273 / 300 = 0.91.Step 10: Therefore percentage error = 0.91 * 100 = 91 percent.Verification / Alternative check:We can also pick a simple value for N, such as N = 10. The correct result is 10 * (10/3) = 100/3 ≈ 33.33. The wrong result is 10 * (3/10) = 3. The error is 33.33 - 3 = 30.33. The percentage error is (30.33 / 33.33) * 100 ≈ 91 percent. This numeric check aligns with the algebraic calculation and confirms the result.Why Other Options Are Wrong:1011.11 percent and 505.56 percent are extremely large and would imply a wrong result many times larger than the correct value, which is not the case here.45.5 percent is roughly half of the actual error and might come from an incorrect partial simplification of the fractions.75 percent is another distractor that is not supported by either algebraic or numeric checks.Common Pitfalls:A common mistake is to compare the difference between 10/3 and 3/10 directly as a percentage of the original number rather than as a percentage of the correct result. Another frequent error is performing fraction arithmetic incorrectly or forgetting that N cancels out when computing relative error. To avoid such issues, always write down the formula for percentage error clearly, simplify the algebra carefully, and, if needed, verify the answer with a simple numerical example.Final Answer:The percentage error in the student's calculation is 91 percent.

Question 4

The cost price of an article is x rupees. It is marked up by 120% above cost and then sold after giving a 20% discount on the marked price. If the final selling price is Rs. 8800, what is the value of x?

Accepted Answer

Introduction / Context:This question connects cost price, marked price, discount, and selling price. It is a typical profit and loss problem where multiple percentage changes occur in sequence. Being able to translate such a description into a clear algebraic expression is important for many competitive examinations and practical business calculations.Given Data / Assumptions:Cost price (CP) of the article = x rupees.The article is marked up by 120% above CP.A 20% discount is then given on the marked price.The final selling price (SP) after discount = Rs. 8800.We need to find the cost price x.Concept / Approach:First, we convert the markup into a multiplier for the cost price. A markup of 120% means the marked price is equal to CP plus 120% of CP, which is 2.2 times CP. Next, a 20% discount on the marked price leaves 80% of that marked price as the selling price. Thus, SP = marked price * 0.8 = 2.2 * CP * 0.8. With SP given as 8800, we can solve for CP using a simple algebraic equation. This chain of multiplicative factors is the key idea.Step-by-Step Solution:Step 1: Marked price (MP) after 120% markup on cost price x: MP = x + 1.2 * x = 2.2 * x.Step 2: Discount of 20% on MP means the selling price SP = MP * (1 - 20/100) = MP * 0.8.Step 3: Substitute MP: SP = 2.2 * x * 0.8 = 1.76 * x.Step 4: We are told SP = Rs. 8800, so 1.76 * x = 8800.Step 5: Solve for x: x = 8800 / 1.76.Step 6: Compute the value: 8800 / 1.76 = 5000, so the cost price x is Rs. 5000.Verification / Alternative check:Verify by reconstructing the entire process from CP = Rs. 5000. Marked price = 2.2 * 5000 = Rs. 11,000. A 20% discount on 11,000 is 11,000 * 20 / 100 = 2200, so the selling price is 11,000 - 2200 = 8800 rupees. This matches the given selling price in the question, confirming that our cost price is correct.Why Other Options Are Wrong:If x = 7680, then MP would be 2.2 * 7680, and after 20% discount the selling price would be different from 8800.Similarly, x = 6000 or x = 6680 would lead to selling prices that do not equal 8800 when the markup and discount are applied.4400 as cost price also fails to produce 8800 rupees under the given percentage operations.Common Pitfalls:A frequent mistake is to treat the markup and discount as additive instead of multiplicative effects or to apply the 20% discount on cost price instead of the marked price. Another common error is to misunderstand the 120% markup as making the marked price 120% of cost price instead of 220% of cost price. To avoid such issues, always express markups and discounts as clear multipliers relative to the appropriate base value, and then chain them carefully in the correct order.Final Answer:The cost price x of the article is Rs. 5000.

Question 5

When a number is increased by 105, it becomes 135% of its original value. What is the original number?

Accepted Answer

Introduction / Context:This question again tests your ability to interpret a verbal description of a percentage increase and convert it into an algebraic equation. The information links the increase in absolute terms to a statement about the final value being a fixed percentage of the original. Solving such problems is a basic yet important part of percentage based aptitude questions.Given Data / Assumptions:Let the original number be N.When the number is increased by 105, the result becomes 135% of the original number.We have to determine the value of N.Concept / Approach:If the original number is N, then a 35% increase leads to a final value of 1.35 * N, which represents 135% of N. The statement in the question can be written as N + 105 = 1.35 * N. This is a simple linear equation in N. Once we solve for N, we can check the result by substituting it back into the condition given.Step-by-Step Solution:Step 1: Let the original number be N.Step 2: After increasing N by 105, the new value is N + 105.Step 3: According to the question, this new value equals 135% of N, that is 1.35 * N.Step 4: Set up the equation: N + 105 = 1.35 * N.Step 5: Rearrange by subtracting N from both sides: 105 = 1.35 * N - N = 0.35 * N.Step 6: Solve for N: N = 105 / 0.35.Step 7: Compute the division: 105 / 0.35 = 300.Verification / Alternative check:To check the result, take N = 300 and calculate 135% of it. 135% of 300 is 300 * 135 / 100 = 300 * 1.35 = 405. Now apply the original condition: if we increase 300 by 105, we get 300 + 105 = 405, which matches 135% of 300. This confirms that the original number must be 300.Why Other Options Are Wrong:If N = 450, then 135% of 450 is 607.5, but 450 + 105 = 555, so the condition fails.If N = 600, then 135% of 600 is 810, but 600 + 105 = 705, so this does not match.If N = 400, then 135% of 400 is 540, but 400 + 105 = 505, which again does not satisfy the equation.210 as a value gives 135% equal to 283.5, while 210 + 105 = 315, which is not the same.Common Pitfalls:Students sometimes misinterpret the phrase "becomes 135% of itself" and treat 135 as the increase instead of 35. Others incorrectly set up the equation as 105 = 1.35 * N, ignoring the original N that must be added. Always express the final amount as original + change and also as original multiplied by the given percentage factor. Equating these two expressions leads directly to the correct equation for N.Final Answer:The original number is 300.

Question 6

The marked price of a shirt is Rs. 100 and the marked price of a pair of trousers is Rs. 300. A 10% discount is given on the shirt and a 20% discount is given on each pair of trousers. If Pritam buys 1 shirt and 3 pairs of trousers, what is the over…

Accepted Answer

Introduction / Context:This question involves different discount rates applied to different items in a single purchase. The goal is to determine the effective discount percentage on the total bill for Pritam. This scenario is very common in real shopping cases where different products have different offers and is frequently tested in percentage and profit and loss sections of aptitude exams.Given Data / Assumptions:Marked price of one shirt = Rs. 100.Marked price of one pair of trousers = Rs. 300.Discount on the shirt = 10% of its marked price.Discount on each pair of trousers = 20% of its marked price.Pritam buys 1 shirt and 3 pairs of trousers.Concept / Approach:The effective discount percentage is based on the total marked price for all items and the total amount actually paid after item wise discounts. We first compute the total marked price. Then we calculate the discounted price for the shirt and the trousers separately, sum these to get the actual payment, and finally compute the overall discount percentage using the formula effective discount = (total marked price - total paid) / total marked price * 100.Step-by-Step Solution:Step 1: Compute the total marked price.Marked price for 1 shirt = 1 * 100 = Rs. 100.Marked price for 3 trousers = 3 * 300 = Rs. 900.Total marked price = 100 + 900 = Rs. 1,000.Step 2: Compute actual payment for the shirt.Discount on shirt = 10% of 100 = 10, so shirt price after discount = 100 - 10 = Rs. 90.Step 3: Compute actual payment for the trousers.Discount per trouser = 20% of 300 = 60, so price after discount for one trouser = 300 - 60 = 240.Step 4: Total for 3 trousers after discount = 3 * 240 = Rs. 720.Step 5: Total amount actually paid by Pritam = 90 + 720 = Rs. 810.Step 6: Total discount amount = total marked price - total paid = 1,000 - 810 = Rs. 190.Step 7: Effective discount percentage = (190 / 1,000) * 100 = 19.Verification / Alternative check:You can also think in terms of average discount per rupee. Pritam saves Rs. 190 out of a possible Rs. 1,000 total marked price. That is a saving of 0.19 rupees per rupee of marked value, which directly translates to a 19% discount. This quick check confirms that our detailed calculation is consistent.Why Other Options Are Wrong:18 percent and 17 percent would both imply smaller total discounts than Rs. 190 on a marked price of Rs. 1,000.16 percent corresponds to a discount of only Rs. 160, which contradicts the actual discount calculations.20 percent discount would require Rs. 200 off, but the actual savings are Rs. 190, so that is also incorrect.Common Pitfalls:Some candidates mistakenly average the two discount rates of 10% and 20%, which does not work because the shirt and trousers contribute different amounts to the total price. Others forget to multiply the discounted price of one trouser by three. The safe strategy is to compute marked price and discounted price for each type of item individually, sum the totals, and then calculate the overall discount percentage from the combined figures.Final Answer:Pritam receives an overall effective discount of 19 percent on his total purchase.

Question 7

The edge length of a cube is increased by 10%. By what percentage does the volume of the cube increase as a result of this change?

Accepted Answer

Introduction / Context:This question tests spatial and percentage reasoning by connecting the linear dimension of a cube (its edge length) with its volume. When a side length changes by a certain percentage, the volume, which depends on the cube of the side length, changes by a different percentage. Understanding this relationship is vital in geometry and in many real world applications involving scaling.Given Data / Assumptions:The original edge length of the cube is assumed to be a units.The edge length is increased by 10%.The volume of a cube is equal to side^3.We must find the percentage increase in volume after the side length increases by 10%.Concept / Approach:If the original side length is a, the original volume is a^3. When the side length is increased by 10%, the new side length becomes a * 1.10. The new volume is then (1.10 * a)^3. To find the percentage change in volume, we compare the new volume with the original volume and compute (new volume - original volume) / original volume * 100. This problem demonstrates that a linear increase leads to a larger multiplicative change in volume because of the cubic relationship.Step-by-Step Solution:Step 1: Let the original edge length be a, so original volume V1 = a^3.Step 2: After a 10% increase, the new edge length is a * (1 + 10/100) = 1.10 * a.Step 3: New volume V2 = (1.10 * a)^3.Step 4: Expand the cube: V2 = 1.10^3 * a^3.Step 5: Compute 1.10^3 = 1.10 * 1.10 * 1.10 = 1.331.Step 6: So V2 = 1.331 * a^3.Step 7: Increase in volume = V2 - V1 = 1.331 * a^3 - 1 * a^3 = 0.331 * a^3.Step 8: Percentage increase in volume = (0.331 * a^3 / a^3) * 100 = 0.331 * 100 = 33.1 percent.Verification / Alternative check:We can verify using a simple numerical value. Take a = 10 units. Original volume V1 = 10^3 = 1,000 cubic units. New side length after 10% increase is 11 units. New volume V2 = 11^3 = 1,331 cubic units. The increase in volume is 1,331 - 1,000 = 331 cubic units. As a percentage of the original volume, this is 331 / 1,000 * 100 = 33.1 percent. This matches the algebraic solution exactly.Why Other Options Are Wrong:30 percent and 31.3 percent underestimate the true cubic effect of the side increase and therefore give too small a percentage change in volume.136.1 percent is far too large and would correspond to more than doubling the volume, which does not happen with a modest 10% side increase.10 percent corresponds only to the change in side length, not to the change in volume, and so it is not the correct answer for this question.Common Pitfalls:Many students incorrectly assume that the volume increases by the same percentage as the side length, that is 10%, or mistake the volume increase as proportional to the square of the change instead of the cube. Another error is to forget to cube the factor 1.10 when computing the new volume. The safe approach is always to express the new dimension as a multiplier of the old one, then raise this multiplier to the appropriate power in the formula and finally compute the resulting percentage change relative to the original value.Final Answer:The volume of the cube increases by 33.1 percent when its edge length is increased by 10 percent.

Question 8

In a clothing sale, if 2 T-shirts are offered free on the purchase of 5 T-shirts at the same marked price, what is the effective percentage discount on each T-shirt for the customer?

Accepted Answer

Introduction / Context: This percentage based aptitude question tests the idea of effective discount when free items are given as part of a promotional offer. Instead of directly cutting the marked price, the shop offers additional T-shirts free with a fixed number of paid T-shirts. Many students confuse such offers with simple percentage discount, so understanding the relation between number of items received and money actually paid is very important for banking, SSC and other competitive exams. Given Data / Assumptions: A customer buys 5 T-shirts and gets 2 T-shirts free in the same offer. All 7 T-shirts have the same marked price per T-shirt. The customer pays only for 5 T-shirts and receives 7 T-shirts in total. We assume the marked price of each T-shirt to be the same convenient value to compute the effective discount percentage. Concept / Approach: The key concept is that effective discount equals reduction in price per unit, expressed as a percentage of the marked price. When free units are bundled, the customer receives more quantity for the same amount of money. We take an assumed marked price, calculate what the customer would pay without any offer, then compare it with the effective cost per T-shirt under the offer. Finally, we compute the percentage discount as (marked price − effective price) / marked price * 100. Choosing a simple assumed marked price, like Rs 100 per T-shirt, keeps the calculation easy without changing the percentage result. Step-by-Step Solution: Step 1: Assume the marked price of each T-shirt is Rs 100 (any convenient value works). Step 2: Without offer, to get 7 T-shirts, the customer would pay 7 * 100 = Rs 700. Step 3: Under the offer, the customer pays for only 5 T-shirts: 5 * 100 = Rs 500, but receives 7 T-shirts. Step 4: Effective price per T-shirt under the offer = total amount paid / total T-shirts received = 500 / 7 ≈ Rs 71.43. Step 5: Discount per T-shirt = marked price − effective price = 100 − 71.43 ≈ 28.57. Step 6: Effective discount percentage = (28.57 / 100) * 100% ≈ 28.57% = 28 4/7%. Verification / Alternative check: An alternate way is to view the offer as giving 2 free out of 7 T-shirts. Fraction of free T-shirts = 2/7. Therefore effective discount = (2/7) * 100% = 200/7% = 28 4/7%. This matches our earlier calculation based on rupee values, confirming that the assumed price method is valid and that the effective discount does not depend on the actual marked price of each T-shirt. Why Other Options Are Wrong: 40% assumes 2 free out of 5, which ignores that the customer actually receives 7 T-shirts. 20% would be correct if only 1 out of 5 were free, which is not the case here. 30% is a rough guess close to the correct value but not mathematically accurate. 25% would correspond to 1 free out of 4 T-shirts or similar offers, which again does not match this situation. Common Pitfalls: Students often divide 2 by 5 instead of 2 by 7 and conclude that the discount is 40%, which is incorrect because they ignore the total number of T-shirts received. Another common error is to treat the offer as a direct reduction in price, without relating it to the per unit cost. Some test takers also forget that percentages should be calculated on the marked price of one item, not on the number of items paid for. Careful identification of the base quantity is essential in discount questions involving free items. Final Answer: The effective discount on each T-shirt is 28 4/7%.

Question 9

A shopkeeper offers three successive discounts of 20%, 10% and 5% on the marked price of an article. What single equivalent rate of discount is equal to this series of discounts?

Accepted Answer

Introduction / Context: This problem checks understanding of successive discounts and how they combine into one overall or single equivalent discount. In real life, shops frequently announce multiple discounts one after another, and many customers incorrectly add the percentages. For competitive exams, it is important to know that successive discounts are multiplicative on the remaining price, not additive on the original price. The question asks you to convert three successive discounts into one equivalent discount rate that gives the same final selling price. Given Data / Assumptions: Let the marked price of the article be M rupees. First discount: 20% on the marked price. Second discount: 10% on the reduced price after the first discount. Third discount: 5% on the reduced price after the second discount. We need one equivalent discount D% such that applying D% once to M gives the same final selling price. Concept / Approach: Successive discounts are applied step by step on the reduced price. If a discount of d% is offered, the remaining price factor is (1 − d/100). For multiple discounts, these factors are multiplied. Once we know the final factor multiplying the marked price, we can convert it back into a single equivalent discount by subtracting the factor from 1 and converting the result into a percentage. This approach avoids the common mistake of simply adding the percentage values of discounts, which is always wrong for successive discounts. Step-by-Step Solution: Step 1: Let the marked price be M. Step 2: After first discount of 20%, price factor = 1 − 20/100 = 0.8. New price = 0.8M. Step 3: After second discount of 10%, factor = 1 − 10/100 = 0.9. New price = 0.8M * 0.9 = 0.72M. Step 4: After third discount of 5%, factor = 1 − 5/100 = 0.95. Final selling price = 0.72M * 0.95 = 0.684M. Step 5: The final factor 0.684 means the customer pays 68.4% of marked price. Step 6: Therefore equivalent single discount = (1 − 0.684) * 100% = 0.316 * 100% = 31.6%. Verification / Alternative check: As a quick check, note that the sum of given discounts is 20% + 10% + 5% = 35%, so the effective discount must be slightly less than 35%, because each later discount is applied to a smaller base. The answer 31.6% is less than 35% and is close to typical exam values, confirming that our calculations are reasonable. Recomputing the multiplication of factors 0.8, 0.9 and 0.95 gives 0.684 again, so the result is consistent. Why Other Options Are Wrong: 31.5% is very close but does not match the exact computed discount of 31.6%. 31% is smaller than the true discount and would produce a slightly higher selling price. 31.4% is also close but still differs from the exact value 31.6% obtained from the product 0.8 * 0.9 * 0.95. Common Pitfalls: The biggest mistake is to simply add the discounts and say 20% + 10% + 5% = 35%, which ignores compounding. Another error is to apply each discount on the original marked price instead of the reduced price. Some students also round intermediate values too early, which can disturb the final answer in close options. Always multiply the remaining fractions step by step and convert the final factor into a single equivalent discount at the end. Final Answer: The single equivalent rate of discount is 31.6%.

Question 10

A basket initially contains 300 mangoes. If 75 mangoes are distributed among some students, what percentage of mangoes remain in the basket afterward?

Accepted Answer

Introduction / Context: This question examines the basic use of percentages to express a remaining quantity after distributing or removing some part of a whole. Such problems are common in aptitude exams and reinforce the idea that percentage is just a ratio multiplied by 100. Understanding how to convert a fraction of remaining items into a percentage helps in many data interpretation and arithmetic questions that involve stocks, inventory and simple distribution scenarios. Given Data / Assumptions: Total number of mangoes in the basket initially = 300. Mangoes distributed among students = 75. Mangoes left in the basket = total mangoes − distributed mangoes. We are required to find the percentage of mangoes left relative to the initial total of 300 mangoes. Concept / Approach: The key idea is to find the remaining quantity and then convert that remaining quantity into a percentage of the original total. To get the remaining quantity, subtract the number of distributed mangoes from the initial number of mangoes. Then, the percentage remaining is (remaining number / original number) * 100. This approach is a straightforward application of the percentage formula and does not require any advanced tricks, making it a classic easy level problem. Step-by-Step Solution: Step 1: Initial number of mangoes in the basket = 300. Step 2: Number of mangoes distributed = 75. Step 3: Mangoes remaining in the basket = 300 − 75 = 225. Step 4: Required percentage of mangoes left = (remaining / original) * 100. Step 5: Percentage remaining = (225 / 300) * 100. Step 6: Simplify the fraction 225 / 300 = 3/4, so percentage = (3/4) * 100 = 75%. Verification / Alternative check: Another quick way is to find what fraction 75 is of 300. Since 75 / 300 = 1/4, we can see that 25% of the mangoes were distributed. If 25% were distributed, the remaining percentage must be 100% − 25% = 75%. This matches the earlier result from direct calculation and confirms that the answer 75% is correct and consistent from both perspectives. Why Other Options Are Wrong: 70% would correspond to 30% of the mangoes being distributed, which would be 90 mangoes, not 75. 72% would mean 28% distribution, equal to 84 mangoes, which again does not match the given data. 76% would imply only 24% distribution, equal to 72 mangoes, which is close but not exact. Common Pitfalls: A common mistake is to miscalculate the remaining mangoes, for example by adding instead of subtracting. Another error is handling the fraction to percentage step incorrectly, often due to arithmetic mistakes in division or multiplication. Some students also mistakenly compute 75 / 225 instead of 225 / 300. Always remember that the denominator in percentage calculation is the original total quantity unless the question explicitly states otherwise. Final Answer: The percentage of mangoes left in the basket is 75%.

Question 11

What is the numerical difference between the decimal number 0.6 and its percentage form 0.6% expressed as a decimal?

Accepted Answer

Introduction / Context: This question tests the understanding of the difference between a decimal number and the same number interpreted as a percentage. Many learners confuse 0.6 with 0.6%, even though they represent very different magnitudes. Being able to convert percentages to decimals and vice versa is fundamental to solving a wide variety of aptitude and data interpretation problems, including profit and loss, interest, and ratio questions. Given Data / Assumptions: We have a decimal number 0.6. We also have 0.6% which is a percentage. We must first convert 0.6% into a decimal form. Then we must calculate the difference between 0.6 and 0.6% expressed as a decimal number. Concept / Approach: To convert a percentage to a decimal, we divide by 100. So x% = x / 100 in decimal form. Therefore, 0.6% is not 0.6, but 0.6 / 100. Once both quantities are in decimal form, we subtract the smaller from the larger to find the numerical difference. In this question, 0.6 is much larger than 0.6%, so the difference should be just slightly less than 0.6. This conceptual expectation helps verify the final calculation. Step-by-Step Solution: Step 1: Write 0.6 as a decimal. It is already in decimal form: 0.6. Step 2: Convert 0.6% to decimal form. Use the formula: percentage / 100. Step 3: 0.6% as decimal = 0.6 / 100 = 0.006. Step 4: Now find the difference between 0.6 and 0.006. Step 5: Difference = 0.6 − 0.006 = 0.594. Step 6: Therefore, the required difference is 0.594. Verification / Alternative check: As a quick sense check, note that 0.6 is 600 times larger than 0.001, while 0.6% equals 0.006, which is only 1% of 0.6. So the difference should be close to 0.6, but slightly smaller. Our computed value 0.594 is indeed close to 0.6 and reasonable. If 0.6% had been incorrectly taken as 0.6, then the difference would have been 0, which clearly makes no sense because the question is contrasting a decimal with a percentage. Why Other Options Are Wrong: 5.94 is ten times larger than 0.594 and would arise from wrongly multiplying instead of dividing by 10. 60 is obtained by multiplying by 100 instead of dividing, which is the opposite of what is required. 54 is also from confusing percentage and decimal positioning, and it ignores the actual scale of the numbers given. Common Pitfalls: A major mistake is treating 0.6% as 0.6, overlooking the division by 100. Another pitfall is misplacing the decimal point when converting from percent to decimal, for example writing 0.06 instead of 0.006. Some learners also reverse the order of subtraction, which would give a negative result, whereas the question simply asks for the difference, typically understood as a positive quantity. Careful conversion and consistent handling of decimals are essential. Final Answer: The difference between 0.6 and 0.6% is 0.594.

Question 12

The salary of a person is first decreased by 50% and is then increased by 50%. By what percentage does the person finally lose from the original salary?

Accepted Answer

Introduction / Context: This question explores the effect of successive percentage changes, specifically a decrease followed by an increase of the same percentage. Many people wrongly assume that a 50% decrease followed by a 50% increase brings the salary back to the original value, but that is not correct. Such problems highlight the non additive nature of percentage changes and are very common in aptitude tests involving income, salary revisions and price fluctuations. Given Data / Assumptions: Initial salary of the person is some amount, say S rupees. First, the salary is decreased by 50%. Then the reduced salary is increased by 50%. We need to find the net percentage loss relative to the original salary S. Concept / Approach: When a quantity changes by a percentage, the new value is original * (1 ± rate/100). Successive changes are handled by multiplying these factors. If the salary is reduced by 50%, the factor is 1 − 50/100 = 0.5. When increased by 50% afterward, the factor is 1 + 50/100 = 1.5, but this applies to the reduced salary. Multiplying 0.5 and 1.5 gives the overall factor. The net percentage change is then found by comparing this final factor with 1 (the original value factor). Step-by-Step Solution: Step 1: Let original salary be S. Step 2: After a 50% decrease, new salary = S * (1 − 50/100) = S * 0.5 = 0.5S. Step 3: This reduced salary is then increased by 50%. So final salary = 0.5S * (1 + 50/100) = 0.5S * 1.5. Step 4: Multiply the factors: 0.5 * 1.5 = 0.75. Final salary = 0.75S. Step 5: Compare final salary with original salary. Loss = S − 0.75S = 0.25S. Step 6: Percentage loss = (0.25S / S) * 100% = 25%. Verification / Alternative check: Take a simple numerical example. Suppose the original salary is Rs 100. After a 50% decrease, salary becomes Rs 50. A 50% increase on Rs 50 gives 50 + 25 = Rs 75. So the person ends up with Rs 75 instead of Rs 100. The loss is Rs 25 on Rs 100, which is 25%. This concrete example supports the algebraic method and shows clearly that the salary does not return to its original value. Why Other Options Are Wrong: 50% would mean the final salary is zero, which is not the case. 75% loss would give a salary of only 25% of the original, which is far too extreme. No loss would mistakenly assume that opposite percentage changes cancel each other, which is only true if applied to the same base value, not successively. Common Pitfalls: Many students simply add or subtract percentages, concluding that a 50% decrease and a 50% increase cancel out. This ignores that the second change is applied to a modified amount. Another mistake is calculating the second 50% on the original salary instead of the reduced one. Always remember that when percentages are applied one after the other, you must multiply the corresponding factors and then compare the final value to the original to get the net effect. Final Answer: The person suffers a net loss of 25% of the original salary.

Question 13

When a number is increased by 120, it becomes 130% of its original value. What is the original number?

Accepted Answer

Introduction / Context: This question deals with converting a word statement involving percentage increase into an algebraic equation. When a number is said to become 130% of itself, it means the new value equals 1.3 times the original number. Such problems are common in percentage and profit and loss chapters, where we often move between absolute changes and percentage descriptions. Proper translation into equations makes these questions straightforward to solve. Given Data / Assumptions: Let the original number be N. When increased by 120, the new number is N + 120. This new value N + 120 equals 130% of the original number. 130% of N means (130/100) * N = 1.3N. We are required to find the numerical value of N. Concept / Approach: The key idea is to set up an equation based on the statement that the new value equals 130% of the original. Once the equation is formed, solving for N reduces to simple algebra. Specifically, we equate N + 120 to 1.3N, then isolate N by moving all terms with N to one side and constants to the other. This pattern repeats in many similar percentage increase or salary raise problems. Step-by-Step Solution: Step 1: Let the original number be N. Step 2: After an increase of 120, the new value is N + 120. Step 3: According to the question, N + 120 = 130% of N = 1.3N. Step 4: Write the equation: N + 120 = 1.3N. Step 5: Rearrange terms: 120 = 1.3N − N = 0.3N. Step 6: Solve for N: N = 120 / 0.3 = 400. Verification / Alternative check: Substitute N = 400 back into the condition. Increasing 400 by 120 gives 400 + 120 = 520. Now calculate 130% of 400: (130/100) * 400 = 1.3 * 400 = 520. Since both methods give the same new value, 520, the solution N = 400 satisfies the condition perfectly. This confirms that our algebraic manipulation is correct and that the original number is indeed 400. Why Other Options Are Wrong: 520 is the new value after increase, not the original number. 460 would give 460 + 120 = 580, but 130% of 460 is 598, which does not match. 580 would produce 580 + 120 = 700, while 130% of 580 is 754, so it clearly fails the given condition. Common Pitfalls: Learners sometimes treat 130% as 130N instead of 1.3N or (130/100) * N. Another frequent error is to set the equation incorrectly as N + 120 = 0.3N, mixing up the meaning of percentage. Care must also be taken with decimal division, since 120 / 0.3 equals 400, not 40. Writing all steps clearly and checking the final answer by substitution is a good habit to avoid such mistakes. Final Answer: The original number is 400.

Question 14

A dealer marks his goods at 20% above the cost price and then allows a discount so that he finally makes a profit of 8%. What is the rate of discount he must offer on the marked price?

Accepted Answer

Introduction / Context: This question connects cost price, marked price, discount and profit percentage. It represents a typical shopkeeper scenario where articles are first marked up from cost and then sold after giving some discount. To solve such problems, students must clearly understand the relation between these quantities and form equations using percentage factors. The aim here is to find the discount rate that converts a 20% markup into an effective profit of 8% after discount. Given Data / Assumptions: Let the cost price (CP) of the article be C rupees. Marked price (MP) is 20% above CP, so MP = C * (1 + 20/100) = 1.2C. After allowing some discount on MP, the article is sold at a selling price (SP) that yields an 8% profit on CP. Thus SP = C * (1 + 8/100) = 1.08C. If discount rate is d%, then SP = MP * (1 − d/100). Concept / Approach: We equate the two expressions for SP. On one side, SP equals 1.08C from the profit condition. On the other side, SP equals 1.2C * (1 − d/100) from the discount condition. By solving this equation for d, we obtain the required discount rate. The method uses the idea that the cost price is the base for profit, while the marked price is the base for discount, and these two are connected through the relationships described above. Step-by-Step Solution: Step 1: Assume cost price = C. Step 2: Marked price = C * (1 + 20/100) = 1.2C. Step 3: Desired selling price for 8% profit = C * (1 + 8/100) = 1.08C. Step 4: Let discount rate on marked price be d%. Then SP = MP * (1 − d/100) = 1.2C * (1 − d/100). Step 5: Equate SP expressions: 1.2C * (1 − d/100) = 1.08C. Step 6: Cancel C: 1.2 * (1 − d/100) = 1.08. So (1 − d/100) = 1.08 / 1.2 = 0.9. Step 7: Therefore 1 − d/100 = 0.9 implies d/100 = 0.1, so d = 10%. Verification / Alternative check: Take C = Rs 100 for simplicity. Then MP = 1.2 * 100 = Rs 120. Discount of 10% on Rs 120 is Rs 12, so SP = 120 − 12 = Rs 108. Profit = SP − CP = 108 − 100 = Rs 8, which is 8% of 100. This matches the required profit percentage and confirms that a 10% discount on the marked price is correct. Why Other Options Are Wrong: 4% discount would give SP = 1.2C * 0.96 = 1.152C, which is a 15.2% profit, not 8%. 6% discount leads to SP = 1.2C * 0.94 = 1.128C, equal to 12.8% profit. 12% discount gives SP = 1.2C * 0.88 = 1.056C, which is only 5.6% profit. Common Pitfalls: Students often mistakenly apply the discount to the cost price instead of the marked price. Another error is to mix up profit percent and discount percent bases and try to add or subtract them directly. Some also assume that if markup is 20% and net profit is 8%, then discount is simply 12%, which ignores compounding via multiplication of factors. Always base calculations on clear algebraic equations relating CP, MP, discount and SP. Final Answer: The discount rate that the dealer must offer is 10%.

Question 15

The sum of two numbers is three times their difference. What is the ratio of the two numbers?

Accepted Answer

Introduction / Context: This question tests basic algebraic manipulation and understanding of ratios. When a relationship is given between the sum and the difference of two numbers, we can express both conditions in terms of the unknowns and derive their ratio. Problems of this type appear frequently in aptitude tests because they check the ability to form and solve simple linear equations and to interpret the result as a ratio rather than as individual numerical values. Given Data / Assumptions: Let the two numbers be A and B. We can assume A is greater than B for simplicity (A > B). The sum of the numbers is A + B. The difference of the numbers is A − B. Given condition: sum is three times the difference, that is A + B = 3(A − B). Concept / Approach: We use algebra to translate the word relation into an equation and then solve for the ratio A:B. Ratios are scale free, so we do not need actual values of A and B. Instead, we simplify the equation to find A/B. Once this fraction is simplified, it directly gives the ratio in its simplest form. This method is common in questions about number relationships, ages and mixtures. Step-by-Step Solution: Step 1: Let the two numbers be A and B with A > B. Step 2: Given that sum is three times the difference, write A + B = 3(A − B). Step 3: Expand the right side: A + B = 3A − 3B. Step 4: Bring all terms involving A and B to one side. Move A and B from left to right or vice versa. Step 5: Subtract A from both sides: B = 2A − 3B. Step 6: Add 3B to both sides: B + 3B = 2A, so 4B = 2A. Step 7: Divide both sides by 2: 2B = A, or A/B = 2/1. Step 8: Therefore, the ratio A:B = 2:1. Verification / Alternative check: Choose concrete numbers that follow the ratio 2:1, for example A = 20 and B = 10. Their sum is 20 + 10 = 30. Their difference is 20 − 10 = 10. The sum 30 is exactly three times the difference 10. This verifies that the ratio 2:1 satisfies the condition and confirms the algebraic result. Why Other Options Are Wrong: 1:2 would give numbers where the smaller number comes first, and it does not satisfy the equation A + B = 3(A − B). 3:1 leads to a different relationship where the sum would not be three times the difference; checking with sample numbers quickly disproves it. 1:3 is the extreme opposite and clearly fails the condition since the larger number must be at least as large as the sum relation implies. Common Pitfalls: A common mistake is to mishandle signs when expanding and rearranging the equation, especially when moving B terms across the equality. Some students also confuse the ratio A:B with B:A and may choose 1:2 instead of 2:1. Another error is to try random trial numbers without first ensuring they satisfy the algebraic condition. Writing each algebraic step carefully helps avoid these issues. Final Answer: The ratio of the two numbers is 2:1.

Question 16

The salary of A is 50% more than the salary of B. By what percentage is the salary of B less than the salary of A?

Accepted Answer

Introduction / Context: This question stresses a very important point in percentage comparison: if one quantity is 50% more than another, the reverse comparison is not 50% less. Many exam questions are designed to expose this misconception. Here, the salary of A is given as 50% more than that of B, and we must compute how much less B earns compared to A, expressed as a percentage of A's salary. Given Data / Assumptions: Let the salary of B be B rupees. The salary of A is 50% more than B, so salary of A = B * (1 + 50/100) = 1.5B. We need to find the percentage by which B is less than A. Required percentage is calculated with A's salary as the base value. Concept / Approach: To find how much B is less than A in percentage terms, we first compute the absolute difference, which is A − B. Then we divide this difference by A (the reference quantity) and multiply by 100 to get the required percentage. Because the base of comparison is different in the two directions, the percentage more and percentage less are not equal. Converting the relationship into simple algebra avoids confusion and gives a precise answer. Step-by-Step Solution: Step 1: Assume salary of B = B rupees. Step 2: Salary of A is 50% more than B, so A = B * 1.5 = 1.5B. Step 3: Difference in salaries = A − B = 1.5B − B = 0.5B. Step 4: Percentage by which B is less than A = (difference / A) * 100. Step 5: Substitute values: percentage = (0.5B / 1.5B) * 100. Step 6: Simplify the fraction 0.5B / 1.5B = 1/3, so percentage = (1/3) * 100% = 33 1/3%. Verification / Alternative check: Take a simple numeric example. Let B = Rs 100. Then A = 150% of 100 = Rs 150. The difference is 150 − 100 = Rs 50. To express this as a percentage of A's salary, compute 50 / 150 * 100 = 33.33%, which is 33 1/3%. This again shows that B's salary is 33 1/3% less than A's salary and confirms the algebraic method. Why Other Options Are Wrong: 50% would almost imply that B has zero salary relative to A, which is not correct because B still earns two thirds of A's salary. 44% and 46 1/2% are close looking distractors but they do not match the exact fraction 1/3 that emerges from the algebraic calculation. Common Pitfalls: The most common mistake is to assume symmetry and say that if A is 50% more than B, then B is 50% less than A. This ignores that the base for percentage calculation changes. Another error arises from using the wrong base in the formula, for example computing (A − B) / B instead of (A − B) / A when the question clearly asks how much less B is than A. To avoid mistakes, always carefully identify which quantity is taken as 100% in the comparison. Final Answer: The salary of B is 33 1/3% less than the salary of A.

Question 17

A shopkeeper marks his goods at 60% above the cost price and then offers a discount of 10% on the marked price. If the cost price of the goods is Rs 7500, what is the final selling price?

Accepted Answer

Introduction / Context: This question combines markup and discount concepts that frequently appear together in profit and loss chapters. A shopkeeper first increases the price over cost (markup) and then reduces that increased price for customers by giving a discount. The aim is to calculate the final selling price given both percentages and the original cost price. Understanding how to sequence and apply these percentage changes is crucial for solving similar exam problems correctly. Given Data / Assumptions: Cost price (CP) of the goods = Rs 7500. Marked price (MP) is 60% above cost price. Discount offered on marked price = 10%. We need to find the final selling price (SP) after applying the discount. Concept / Approach: We first compute the marked price using the markup percentage based on cost price. That is, MP = CP * (1 + markup/100). Then we apply the discount to the marked price, so SP = MP * (1 − discount/100). It is vital to remember that the discount is applied on the marked price, not on the cost price. Doing these operations step by step avoids confusion and gives the exact selling price. Step-by-Step Solution: Step 1: Given cost price = Rs 7500. Step 2: Markup is 60%, so marked price MP = 7500 * (1 + 60/100) = 7500 * 1.6. Step 3: Calculate marked price: 7500 * 1.6 = 12000. So MP = Rs 12000. Step 4: Discount on MP is 10%, so selling price SP = MP * (1 − 10/100) = 12000 * 0.9. Step 5: Compute SP: 12000 * 0.9 = 10800. Step 6: Therefore, the final selling price after discount is Rs 10800. Verification / Alternative check: We can check the overall effect as a combined factor. Markup factor = 1.6, discount factor = 0.9. Net factor on cost price = 1.6 * 0.9 = 1.44. Apply this directly to CP: SP = 7500 * 1.44 = 10800, which matches the stepwise computation. This confirms that both methods are consistent and that the final answer is correct. Why Other Options Are Wrong: 11800 and 12800 would correspond to different combinations of markup and discount or calculation mistakes. 13800 is even higher, suggesting little or no discount after markup, which does not match the given 10% discount. Common Pitfalls: Some learners mistakenly add percentages directly to the cost price without sequencing, for example trying to apply discount first or using markup minus discount on cost price. Others forget that the discount is always applied to the marked price, not the original cost. Rounding errors are not an issue here since all numbers are clean, but incorrect order of operations can easily lead to wrong answers. Always compute marked price first and then discount it to get the selling price. Final Answer: The final selling price of the goods is Rs 10800.

Question 18

In a firm, the average salary of male employees is Rs 5200 and the average salary of female employees is Rs 4200. The overall average salary of all employees together is Rs 5000. What percentage of the employees are female?

Accepted Answer

Introduction / Context: This question involves weighted averages and percentage composition of a group. The firm has male and female employees with different average salaries and a combined overall average. From these averages, we must determine what fraction or percentage of the employees are female. Such problems are very important in data interpretation, mixture, and statistics type questions where groups are combined with different averages or concentrations. Given Data / Assumptions: Average salary of male employees = Rs 5200. Average salary of female employees = Rs 4200. Overall average salary of all employees = Rs 5000. Let the number of male employees be M and the number of female employees be F. We need to find the percentage of employees who are female, that is (F / (M + F)) * 100. Concept / Approach: The total salary paid to males is 5200 * M and to females is 4200 * F. The overall average of 5000 means that the combined total salary is 5000 * (M + F). So we can write an equation: 5200M + 4200F = 5000(M + F). Solving this equation for the ratio F:M allows us to compute the fraction of female employees. The approach is directly based on the definition of weighted average. Step-by-Step Solution: Step 1: Let number of males be M and number of females be F. Step 2: Total salary of males = 5200M. Step 3: Total salary of females = 4200F. Step 4: Total number of employees = M + F and overall average salary is Rs 5000. Step 5: So total combined salary = 5000(M + F). Step 6: Form equation: 5200M + 4200F = 5000(M + F). Step 7: Expand right side: 5200M + 4200F = 5000M + 5000F. Step 8: Rearrange terms: 5200M − 5000M = 5000F − 4200F. Step 9: This gives 200M = 800F, so dividing both sides by 200 gives M = 4F. Step 10: Therefore, the ratio M:F = 4:1 and F:M = 1:4. Step 11: Fraction of employees who are female = F / (M + F) = 1 / (4 + 1) = 1/5. Step 12: Percentage of female employees = (1/5) * 100% = 20%. Verification / Alternative check: Assume there are 4 males and 1 female as per the ratio. Total salary of males = 4 * 5200 = 20800. Total salary of females = 1 * 4200 = 4200. Combined salary = 20800 + 4200 = 25000. Average for all 5 employees = 25000 / 5 = 5000, which matches the given overall average. So the assumed numbers follow the condition perfectly and confirm that 20% of the employees are female. Why Other Options Are Wrong: 80% female would imply far more females than males, which would pull the overall average salary much closer to Rs 4200, not Rs 5000. 40% or 30% are intermediate incorrect guesses that do not satisfy the weighted average equation and would give a combined average different from Rs 5000. Common Pitfalls: Many students attempt to handle this type of problem intuitively and misjudge the required female percentage. Another error is miswriting the weighted average equation, for instance using 5000M + 5000F on the wrong side or forgetting that the average must be multiplied by the total number of employees. Some aspirants also confuse the ratio M:F with the percentage directly, without converting properly. Writing the equation carefully and solving step by step avoids such mistakes. Final Answer: The percentage of female employees in the firm is 20%.

Question 19

If A = 400 and B = 600, then by what percentage is the value of A less than the value of B?

Accepted Answer

Introduction / Context: This question focuses on relative percentage comparison between two numbers. It asks how much one value is less than another in percentage terms. Such comparisons are useful in real situations like salary differences, price changes and performance comparisons. The key is to identify which quantity is taken as the base for the percentage calculation, because the answer changes if you reverse the base. Given Data / Assumptions: Value of A = 400. Value of B = 600. B is the base quantity since the question asks how much A is less than B. We need to compute percentage difference using the formula: (difference / base) * 100. Concept / Approach: To find how much A is less than B in percentage, first determine the absolute difference B − A. Then divide this difference by B (because B is the reference) and multiply by 100. This yields the required percentage less. It is important not to mistakenly divide by A, which would answer a different question, namely how much B is more than A. Step-by-Step Solution: Step 1: Given A = 400 and B = 600. Step 2: Compute the absolute difference: B − A = 600 − 400 = 200. Step 3: Since we want how much A is less than B, take B as the base. Step 4: Required percentage = (difference / base) * 100 = (200 / 600) * 100. Step 5: Simplify the fraction: 200 / 600 = 1/3. Step 6: Percentage = (1/3) * 100 ≈ 33.33. Verification / Alternative check: We can also see that A is two thirds of B, because 400 / 600 = 2/3. So A is missing one third of B. One third as a percentage is 33.33. Therefore, 400 is 33.33% less than 600. The two methods agree, confirming that the answer is correct. This also shows that if something is two thirds of a reference value, it is 33.33% less than that reference value. Why Other Options Are Wrong: 50 would mean the difference is half of B, but 200 is not half of 600. 66.66 would arise if someone took 400 as base and wrongly computed how much B is more than A instead of how much A is less than B. 25 would correspond to a difference equal to one quarter of B, but 200 is not one quarter of 600. Common Pitfalls: A common error is confusing which quantity should be used as base in the percentage formula. Students sometimes compute (600 − 400) / 400 * 100 and obtain 50, which is actually the percentage by which B is greater than A. Another pitfall is rounding early or forgetting that 1/3 corresponds to 33.33 and not 33 exactly. Always read the wording of the question carefully to decide the correct base quantity, and only then apply the percentage formula. Final Answer: A is 33.33% less than B.

Question 20

The marked price of a ceiling fan is Rs 1200 and the shopkeeper allows a discount of 5% on this marked price. What is the selling price of the fan?

Accepted Answer

Introduction / Context: This basic percentage question involves calculating the selling price of an item after a given discount on its marked price. Such problems are common in the profit and loss section of aptitude exams and mirror everyday shopping situations. Understanding how to compute discount and find the resulting selling price is essential for solving a wide range of commercial arithmetic problems. Given Data / Assumptions: Marked price (MP) of the ceiling fan = Rs 1200. Discount offered on the marked price = 5%. Selling price (SP) is equal to marked price minus discount. We need to find the value of SP after applying the 5% discount. Concept / Approach: To find the selling price after discount, we can either compute the discount amount and subtract it from the marked price, or directly multiply the marked price by (1 − discount/100). In this case, a 5% discount means the customer pays 95% of the marked price. Thus, SP = MP * 95/100. This method is efficient and avoids extra subtraction steps. Step-by-Step Solution: Step 1: Marked price MP = Rs 1200. Step 2: Discount = 5%, so customer pays 100% − 5% = 95% of MP. Step 3: Selling price SP = MP * 95/100. Step 4: Substitute MP = 1200, so SP = 1200 * 95/100. Step 5: Simplify: 1200 * 95/100 = 12 * 95 = 1140. Step 6: Therefore, SP = Rs 1140. Verification / Alternative check: Alternatively, compute the discount amount first. Discount amount = 5% of 1200 = 1200 * 5/100 = 60. Subtract this from the marked price: SP = 1200 − 60 = 1140. This matches the previous method and confirms that our answer is correct. Comparing both approaches also reinforces the flexibility of using either direct percentage multiplication or discount subtraction. Why Other Options Are Wrong: Rs 1410 and Rs 1400 are both higher than the marked price, which is not possible after a discount. Rs 1104 would correspond to a higher discount rate than 5%, so it does not match the given data. Common Pitfalls: A common error is to miscalculate the discount percentage or to apply the discount incorrectly, for example computing 1200 − 1200 * 0.5 instead of 0.05 due to decimal confusion. Some students also mistakenly treat 5% as 0.5 in decimal form. Another problem is forgetting that after discount the selling price must be lower than the marked price. double checking the percentage and the direction of change helps to avoid these errors. Final Answer: The selling price of the fan is Rs 1140.

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