Question 1

A dealer marks a washing machine at Rs 7500 and allows a discount of 6% on the marked price. What is the selling price per washing machine?

Accepted Answer

Introduction / Context: This question is another straightforward application of discount on marked price, but with a slightly different percentage. It reflects everyday retail practices, where the marked price on an item is reduced by a given discount to attract customers. For aptitude exams, being comfortable with computing such discounts quickly and accurately is very important, especially when the numbers are friendly and allow mental calculation. Given Data / Assumptions: Marked price (MP) of the washing machine = Rs 7500. Discount offered = 6% of the marked price. Selling price (SP) is equal to MP minus the discount amount. We must compute SP in rupees. Concept / Approach: As with other discount problems, the selling price after discount can be written directly as SP = MP * (1 − discount/100). For a 6% discount, the customer pays 94% of the marked price. Therefore, SP = 7500 * 94/100. This method avoids separate calculations for discount and subtraction, though we may still verify by both methods to strengthen understanding. Step-by-Step Solution: Step 1: Marked price MP = Rs 7500. Step 2: Discount = 6%, so customer pays 100% − 6% = 94% of MP. Step 3: Selling price SP = MP * 94/100 = 7500 * 94/100. Step 4: Simplify: 7500 * 94/100 = 75 * 94 = 7050. Step 5: Therefore, SP = Rs 7050. Verification / Alternative check: Compute the discount amount explicitly. Discount amount = 6% of 7500 = 7500 * 6/100 = 450. Then SP = marked price − discount amount = 7500 − 450 = 7050. This agrees with the previous method and confirms that the result is correct. The dual verification helps ensure no arithmetic mistake has been made in handling the percentage. Why Other Options Are Wrong: 6850 corresponds to a larger discount than 6%, because 7500 − 6850 = 650, which is about 8.67% of 7500. 7250 would correspond to a discount of only 250, about 3.33%, not the stated 6%. 6950 would give a discount of 550, which is roughly 7.33% of 7500, again different from 6%. Common Pitfalls: Students sometimes confuse 6% with 0.6 or 0.06 and may write the wrong decimal, leading to incorrect discount amounts. Another pitfall is incorrectly multiplying 7500 by 94 and misplacing zeros, for instance computing 7500 * 0.94 as 7040 or 7060. A simple check is to estimate that 6% of 7500 is slightly less than 10% of 7500 (which is 750), so the discount should be around 450 and SP around 7050. Estimation helps catch calculation errors. Final Answer: The selling price of each washing machine is Rs 7050.

Question 2

A motor has 120 machine parts of which 5% are defective. Another motor has 80 machine parts of which 10% are defective. Considering both motors together, what is the overall percentage of defective machine parts?

Accepted Answer

Introduction / Context: This question is about combined percentages over two different groups. Each motor has its own percentage of defective parts and a specific number of parts. To find the overall percentage of defective parts when the two motors are considered together, we must work with actual numbers of defective parts rather than averaging the percentages directly. This concept is important in quality control and data analysis problems where different batches or groups are combined. Given Data / Assumptions: Motor 1 has 120 machine parts and 5% of them are defective. Motor 2 has 80 machine parts and 10% of them are defective. We assume each percentage is calculated correctly for its own motor. We need the overall percentage of defective parts across both motors combined. Concept / Approach: The correct method is to find the total number of defective parts in each motor, sum them, and divide by the total number of parts from both motors. Then we convert that fraction into a percentage. Averaging the two percentages directly (for example, (5% + 10%) / 2) would be wrong because the motors have different total numbers of parts, so their contributions are not equal. Step-by-Step Solution: Step 1: For motor 1, total parts = 120. Defective percentage = 5%. Step 2: Defective parts in motor 1 = 5% of 120 = 120 * 5/100 = 6. Step 3: For motor 2, total parts = 80. Defective percentage = 10%. Step 4: Defective parts in motor 2 = 10% of 80 = 80 * 10/100 = 8. Step 5: Total defective parts in both motors = 6 + 8 = 14. Step 6: Total machine parts in both motors = 120 + 80 = 200. Step 7: Overall defective percentage = (14 / 200) * 100 = 7%. Verification / Alternative check: Another way to sanity check is to note that the combined group has 200 parts and 14 defective parts. Since 10% of 200 would be 20, and we have 14 defective parts, the overall defective percentage must be less than 10%. Likewise, 5% of 200 would be 10, and 14 is slightly above that, so the percentage should be slightly above 5%. The computed value 7% fits comfortably in this range and is reasonable. Why Other Options Are Wrong: 6.5 and 7.5 are close but do not match the exact calculation from 14/200. 8% would correspond to 16 defective parts out of 200, which is more than the actual count of 14. Common Pitfalls: A typical mistake is to average the percentages as (5 + 10)/2 = 7.5 without considering different quantities in each group. This gives a value close to the correct answer but still wrong. Another error is miscalculating the defective parts by applying percentages incorrectly to 120 or 80. Finally, some learners forget to convert the fraction into a percentage by multiplying by 100. Precise stepwise calculation helps avoid these problems. Final Answer: The overall percentage of defective machine parts is 7%.

Question 3

The selling price of an article is Rs 9250 after allowing a discount of 7.5% on the marked price. What is the marked price of the article?

Accepted Answer

Introduction / Context: This question reverses the usual discount calculation. Instead of finding the selling price from the marked price and discount, we are given the selling price and discount rate and asked to find the marked price. Such reverse percentage problems are very common in competitive exams, as they test a deeper understanding of how discounts affect prices and require careful algebraic manipulation rather than one step arithmetic. Given Data / Assumptions: Selling price (SP) after discount = Rs 9250. Discount rate on marked price (MP) = 7.5%. Therefore, the customer pays 100% − 7.5% = 92.5% of the marked price. We need to find MP such that SP = 92.5% of MP. Concept / Approach: The relationship between selling price and marked price under a discount is SP = MP * (1 − discount/100). Here the discount is 7.5%, so SP = MP * 92.5/100. To find MP, we solve this equation: MP = SP * 100 / 92.5. Recognising that 92.5% is 0.925 in decimal form also helps. This approach is standard for reverse discount and reverse percentage problems. Step-by-Step Solution: Step 1: Let marked price be MP. Step 2: Discount rate = 7.5%, so customer pays 92.5% of MP. Step 3: Selling price SP = MP * 92.5/100. Step 4: Given SP = 9250, so 9250 = MP * 92.5/100. Step 5: Rearrange to get MP = 9250 * 100 / 92.5. Step 6: Convert 92.5 to decimal: 92.5 = 92.5. So in decimal form, 92.5/100 = 0.925 and MP = 9250 / 0.925. Step 7: Compute MP: 9250 / 0.925 = 10000. Verification / Alternative check: Check the result by forward calculation. If MP = Rs 10000 and discount = 7.5%, discount amount = 10000 * 7.5/100 = 750. Selling price should then be 10000 − 750 = 9250. This matches the given SP in the question, confirming that our computed marked price is correct. Why Other Options Are Wrong: 9000 and 8556.25 are values lower than the selling price or associated with incorrect manipulation of the discount formula. 9943.75 is close but still not exact; using it as MP would not yield SP exactly equal to 9250 when a 7.5% discount is applied. Common Pitfalls: Some students mistakenly compute MP by subtracting 7.5% from SP, treating SP as if it were the marked price, which leads to a lower and incorrect value. Others misinterpret 7.5% as 0.75 instead of 0.075 or confuse 92.5% with 0.9250 without handling the decimals correctly. To avoid confusion, always write the discount equation clearly and isolate the unknown step by step. Final Answer: The marked price of the article is Rs 10000.

Question 4

A number is decreased by 10% and the result is 54. To make this value equal to 72, by what percentage should 54 be increased?

Accepted Answer

Introduction / Context: This problem combines successive percentage changes and asks for the percentage increase needed to move from one specific value to another. The initial information that the number was decreased by 10% to become 54 is not directly required to find the percentage increase from 54 to 72, but it provides context about how the number changed earlier. Being able to compute percentage increase between two given numbers is a very common skill tested in aptitude examinations. Given Data / Assumptions: After a 10% decrease from some original number, the resulting value is 54. We now want to increase 54 to 72. We are asked for the percentage increase required on 54 to reach 72. The base for the percentage increase calculation is 54. Concept / Approach: Percentage increase is calculated as (increase / original value) * 100. Here the original value for the second change is 54 and the final value is 72. So the increase is 72 − 54 and the percentage increase is (72 − 54) / 54 * 100. The earlier information about a 10% decrease can be used to find the original number if needed, but it is not essential for solving the specific question about the increase from 54 to 72. Step-by-Step Solution: Step 1: Current value = 54. Step 2: Target value = 72. Step 3: Absolute increase required = 72 − 54 = 18. Step 4: Base for percentage calculation = 54. Step 5: Percentage increase = (increase / base) * 100 = (18 / 54) * 100. Step 6: Simplify the fraction 18 / 54 = 1/3. Step 7: Therefore, percentage increase = (1/3) * 100% = 33.33%. Verification / Alternative check: We can also view 72 as a multiple of 54. Compute 72 / 54 = 4/3 ≈ 1.3333. This means 72 is 1.3333 times 54, or 133.33% of 54. The extra above 100% is 33.33%. Thus the required percentage increase is 33.33%, consistent with the previous method. The earlier information about a 10% decrease could be checked: if after a 10% decrease the value is 54, then original number is 54 / 0.9 = 60. But this does not affect the needed increase from 54 to 72. Why Other Options Are Wrong: 25% would give a new value of 54 * 1.25 = 67.5, which is less than 72. 30% would give 54 * 1.3 = 70.2, still short of 72. 20% would produce 54 * 1.2 = 64.8, again too small. 40% would give 54 * 1.4 = 75.6, which exceeds 72. Common Pitfalls: Some students unnecessarily involve the original number before the 10% decrease and attempt a more complex approach. Others mistakenly compute (72 − 54) / 72 instead of dividing by 54, which answers how much smaller 54 is than 72 rather than how much 54 must grow. Another frequent error is rounding 1/3 to 30% or 35% instead of 33.33%. Always carefully identify the correct base for percentage calculations and keep sufficient precision in fractions like 1/3. Final Answer: The value 54 must be increased by 33.33% to become 72.

Question 5

The list price of an article is Rs 900. It is sold after two successive discounts of 20% and 10%. What is the final selling price of the article?

Accepted Answer

Introduction / Context: This question again illustrates successive discounts, but with concrete rupee values. Instead of calculating a single equivalent discount rate, we directly find the final selling price after applying each discount step by step. These situations commonly occur during festive sales or clearance offers, and they are also popular in quantitative aptitude tests to check clarity on repeated percentage reductions. Given Data / Assumptions: List price or marked price of the article = Rs 900. First discount offered = 20% on the list price. Second discount offered = 10% on the already reduced price. We need to find the final selling price after both discounts. Concept / Approach: First, we reduce the marked price by 20% to get an intermediate price. Then we reduce that intermediate price by 10% to get the final selling price. Each discount applies to the price obtained after the previous discount, not to the original list price. The process can also be represented by multiplying by remaining fractions: first 0.8 for 20% discount, then 0.9 for 10% discount, giving an overall factor of 0.72 on the list price. Step-by-Step Solution: Step 1: Initial list price = Rs 900. Step 2: First discount = 20%, so price after first discount = 900 * (1 − 20/100) = 900 * 0.8. Step 3: Compute intermediate price: 900 * 0.8 = 720. Step 4: Second discount = 10% on 720, so final price = 720 * (1 − 10/100) = 720 * 0.9. Step 5: Compute final selling price: 720 * 0.9 = 648. Step 6: Therefore, the final selling price is Rs 648. Verification / Alternative check: Combine both discounts as a single factor first. Remaining fraction after 20% discount is 0.8 and after 10% discount is 0.9. Net factor = 0.8 * 0.9 = 0.72. Applying this directly to the list price: SP = 900 * 0.72 = 648. This matches the stepwise calculation and confirms the correctness of the answer. Why Other Options Are Wrong: Rs 640 and Rs 548 come from incorrect calculations or wrong multipliers. Rs 540 would be correct only if the overall remaining factor were 0.6 instead of 0.72, which would correspond to different discounts. Common Pitfalls: Some candidates mistakenly deduct the second discount from the original list price instead of the discounted price, effectively treating both discounts as independent on the same base. Others wrongly add discounts as 20% + 10% = 30% and then compute 900 * 0.7 = 630, which is incorrect since successive discounts compound multiplicatively. Keeping track of which price each discount applies to helps avoid these errors. Final Answer: The final selling price of the article is Rs 648.

Question 6

A person loses 75% of his money in the first bet, 75% of the remaining money in the second bet, and 75% of the remaining money again in the third bet, and finally returns home with Rs 2. What was his initial amount of money?

Accepted Answer

Introduction / Context: This question deals with repeated percentage losses applied successively to a quantity, in this case money used for betting. Instead of a single reduction, the person repeatedly loses 75% of the current amount. At the end, we are given the final amount left and asked to work backwards to find the original amount. These types of questions highlight how repeated losses compound and how to reverse such processes using inverse operations. Given Data / Assumptions: A person starts with some initial amount of money, say X rupees. In the first bet, he loses 75% of X, so 25% of X remains. In the second bet, he loses 75% of the remaining amount, so only 25% of that remains. In the third bet, he again loses 75% of the current amount, so 25% of that remains. After the third bet, he is left with Rs 2. Concept / Approach: Each loss of 75% means the remaining fraction is 25% or 1/4 of the previous amount. So after the first bet he has X * 1/4, after the second bet he has X * (1/4)^2 and after the third bet he has X * (1/4)^3. This final amount is given as Rs 2. We set up an equation X * (1/4)^3 = 2 and solve for X. Alternatively, we can work backwards by reversing the losses: if 2 is one quarter of the amount before the third bet, then the previous amount was 4 times 2, and so on. Step-by-Step Solution: Step 1: Let initial money be X rupees. Step 2: After first bet, he loses 75%, so he keeps 25%: amount = X * 25/100 = X/4. Step 3: After second bet, again he keeps only 25% of current amount: amount = (X/4) * 1/4 = X/16. Step 4: After third bet, again he keeps only 25%: amount = (X/16) * 1/4 = X/64. Step 5: Given final amount after third bet is X/64 = 2. Step 6: Solve for X: X = 2 * 64 = 128. Verification / Alternative check: Check by forward simulation. Start with Rs 128. After first loss of 75%, remaining money = 25% of 128 = 0.25 * 128 = 32. After second loss of 75%, remaining money = 25% of 32 = 8. After third loss of 75%, remaining money = 25% of 8 = 2. This matches the final amount given in the question, so the initial amount must indeed be Rs 128. Why Other Options Are Wrong: Rs 64 would produce 64 → 16 → 4 → 1, which does not match the final amount of 2. Rs 256 would produce 256 → 64 → 16 → 4, again inconsistent with the required final amount. Rs 512 would give even larger values and still not end at 2 after three 75% losses. Common Pitfalls: Students sometimes try to subtract 75% three times from the original amount as if the loss were always calculated on X instead of the remaining amount. Others misinterpret 75% as leaving 75% instead of 25%. Another mistake is incorrect handling of powers of 1/4, for example using (1/4)^2 when three losses are given. Working with fractions carefully and checking with a forward simulation helps avoid these errors. Final Answer: The person initially had Rs 128.

Question 7

A discount series of 15%, 20% and 25% is allowed successively on the marked price of an article. What single equivalent rate of discount is equal to this series of three discounts?

Accepted Answer

Introduction / Context: This problem extends the idea of successive discounts to three levels: 15%, 20% and 25%. The objective is to find a single discount rate that would produce the same final selling price as applying these three discounts one after the other. Knowing how to combine several percentage reductions into one effective percentage is useful in understanding real life sale offers and is frequently tested in quantitative aptitude exams. Given Data / Assumptions: Let the marked price of the article be M rupees. First discount = 15% on M. Second discount = 20% on the price after the first discount. Third discount = 25% on the price after the second discount. We need a single equivalent discount D% such that applying D% once to M gives the same final selling price. Concept / Approach: If a discount of d% is applied, then the remaining price factor is (1 − d/100). For multiple discounts, the total remaining factor is the product of the individual remaining factors. Here, the remaining factors will be 0.85 for 15%, 0.8 for 20% and 0.75 for 25%. Multiply these to get the final fraction of marked price that the buyer pays. The equivalent single discount is then 1 minus this fraction, converted to a percentage. Step-by-Step Solution: Step 1: Assume marked price = M. Step 2: After 15% discount, remaining fraction = 1 − 15/100 = 0.85. New price = 0.85M. Step 3: After 20% discount on this price, remaining fraction = 1 − 20/100 = 0.8. New price = 0.85M * 0.8 = 0.68M. Step 4: After 25% discount on this price, remaining fraction = 1 − 25/100 = 0.75. Final price = 0.68M * 0.75. Step 5: Multiply: 0.68 * 0.75 = 0.51. So final price = 0.51M. Step 6: This means the customer pays 51% of the marked price, so the single equivalent discount = 100% − 51% = 49%. Verification / Alternative check: We can test with an actual value, for example M = Rs 100. After 15% discount, price = 85. After 20% discount, price = 85 * 0.8 = 68. After 25% discount, price = 68 * 0.75 = 51. Thus the buyer finally pays Rs 51 on a Rs 100 marked price. This clearly shows a total effective discount of 100 − 51 = 49%, which matches the computed value. The numerical test confirms that our algebraic reasoning is correct. Why Other Options Are Wrong: 48% or 50% are close but not equal to the exact discount of 49%; using them would give final prices slightly different from 51% of M. 51% discount would leave only 49% of M as the final price, which reverses the correct result. Common Pitfalls: Many students try to add the discount rates directly as 15% + 20% + 25% = 60%, which gives a greatly exaggerated effective discount. Others apply each discount to the original marked price instead of to the successively reduced prices. Some also commit calculation mistakes when multiplying decimals. To avoid errors, always convert each discount to a remaining factor, multiply them carefully, and only then subtract from 1 to get the equivalent single discount. Final Answer: The single equivalent rate of discount is 49%.

Question 8

If basis points are defined so that 1 percent is equal to 100 basis points, then by how many basis points is 82.5 percent greater than 62.5 percent?

Accepted Answer

Introduction / Context: This percentage question checks understanding of the financial term "basis points" and how to convert a difference in percentages into basis points. Basis points are widely used in banking, loans, and interest rate comparisons, so being comfortable with this conversion is very useful for aptitude exams as well as real life decisions. Given Data / Assumptions: - 1 percent is defined as 100 basis points. - First value: 82.5 percent. - Second value: 62.5 percent. - We must find by how many basis points the first value is greater than the second value. Concept / Approach: The key idea is that the difference between two percentages, measured in percentage points, can be converted into basis points by multiplying by 100. One basis point is 0.01 percent, so 100 basis points make 1 percent. We first compute the difference 82.5 percent minus 62.5 percent and then express that 20 percent gap in basis points. Step-by-Step Solution: Step 1: Calculate the difference in percentages: 82.5 percent - 62.5 percent = 20 percent.Step 2: Recall that 1 percent = 100 basis points.Step 3: Therefore, 20 percent = 20 * 100 basis points.Step 4: 20 * 100 = 2000 basis points.So 82.5 percent is greater than 62.5 percent by 2000 basis points. Verification / Alternative check: You can think in terms of decimal form. The difference is 0.825 - 0.625 = 0.20. One basis point is 0.0001 in decimal form. Dividing 0.20 by 0.0001 gives 0.20 / 0.0001 = 2000. This confirms that the gap is 2000 basis points. Why Other Options Are Wrong: - 0.2: This is far too small; it confuses percentage with basis points scale. - 20: This would only be correct if 1 percent equalled 1 basis point, which is not the definition. - 200: This treats 1 percent as 10 basis points, again inconsistent with the definition. Common Pitfalls: A common error is to confuse percentage points with percent. The question asks for the difference in basis points, not the ratio of the two percentages. Another frequent mistake is to multiply or divide by 10 instead of 100 when converting between percent and basis points. Remember that 1 percent equals 100 basis points, not 10, so always multiply the percent difference by 100 to get basis points. Final Answer: The number of basis points by which 82.5 percent is greater than 62.5 percent is 2000.

Question 9

While selling a watch, a shopkeeper gives a discount of 5 percent on the marked price, and if instead he gives a discount of 7 percent he earns 15 rupees less profit. What is the marked price of the watch?

Accepted Answer

Introduction / Context: This problem tests your understanding of how discounts affect selling price and profit for a fixed marked price. It is a typical percentage question where you must relate two different discount scenarios using a single unknown marked price and interpret a given difference in profit. Given Data / Assumptions: - Marked price of the watch is unknown; let it be M rupees. - In the first case, discount = 5 percent, so selling price is 95 percent of M. - In the second case, discount = 7 percent, so selling price is 93 percent of M. - Profit in the second case is 15 rupees less than in the first case. - Cost price is the same in both cases. Concept / Approach: The cost price does not change between scenarios, so the change in profit equals the change in selling price. Therefore the difference between the two selling prices is 15 rupees. We express both selling prices in terms of the marked price M, form an equation for their difference, and solve for M. No explicit cost price value is required because it cancels out. Step-by-Step Solution: Step 1: First selling price with 5 percent discount: SP1 = 95 percent of M = 0.95 * M.Step 2: Second selling price with 7 percent discount: SP2 = 93 percent of M = 0.93 * M.Step 3: Given that the profit decreases by 15 rupees when the discount goes from 5 percent to 7 percent, the selling price must also decrease by 15 rupees.Step 4: So, SP1 - SP2 = 15.Step 5: Substitute 0.95 * M - 0.93 * M = 15.Step 6: This simplifies to 0.02 * M = 15.Step 7: Therefore M = 15 / 0.02 = 750. Verification / Alternative check: Check quickly by computing selling prices. When M = 750, SP1 = 95 percent of 750 = 0.95 * 750 = 712.5. SP2 = 93 percent of 750 = 0.93 * 750 = 697.5. The difference SP1 - SP2 = 712.5 - 697.5 = 15, which matches the given decrease in profit, confirming that the marked price is correct. Why Other Options Are Wrong: - 697.5: This equals the lower selling price, not the marked price. - 712.5: This equals the higher selling price, not the marked price. - None of the these: This is incorrect because option 750 is a valid and consistent marked price as shown by the calculations. Common Pitfalls: Students sometimes try to involve the cost price directly, which complicates the problem unnecessarily. The essential idea is that profit changes by exactly the same amount as the selling price when the cost price is constant. Another mistake is to treat the 2 percent difference between 5 percent and 7 percent discounts as 2 rupees instead of expressing it as 0.02 times the marked price. Always convert percentage changes into expressions involving the unknown marked price first. Final Answer: The marked price of the watch is 750 rupees.

Question 10

In the last financial year a car company sold 41,800 cars, and in the current year its target is to sell 51,300 cars. By what percentage must the sales be increased to reach the new target?

Accepted Answer

Introduction / Context: This question tests the concept of percentage increase, which is widely used for sales targets, company growth, and population changes. The idea is to compare the new target with the previous year's achievement and compute how much increase is required as a percentage of the original value, not of the new value. Given Data / Assumptions: - Last year's car sales = 41,800 cars. - This year's target sales = 51,300 cars. - We need the percentage increase needed relative to 41,800. - The formula for percentage increase is (Increase / Original) * 100 percent. Concept / Approach: The key concept is to first compute the absolute increase in the number of cars and then express that increase as a percentage of the original sales. We must be careful to divide by the original value (last year's sales), because percentage change is always measured relative to the starting point. Once we get a decimal, we can convert it into a mixed fraction to match the given options. Step-by-Step Solution: Step 1: Calculate the increase in number of cars: Increase = 51,300 - 41,800.Step 2: Increase = 9,500 cars.Step 3: Use the percentage increase formula: Percentage increase = (Increase / Original) * 100.Step 4: Substitute values: Percentage increase = (9,500 / 41,800) * 100.Step 5: Compute the fraction 9,500 / 41,800, which simplifies to 95 / 418.Step 6: Now 95 / 418 * 100 is approximately 22.727 percent.Step 7: 22.727 percent corresponds to 22 8/11 percent when written as a mixed fraction. Verification / Alternative check: To check quickly, convert 22 8/11 percent to a decimal. Since 8/11 is approximately 0.727, 22 8/11 percent is about 22.727 percent. Multiply 41,800 by 22.727 percent (0.22727) to see if the increase is roughly 9,500 cars. 41,800 * 0.22727 is close to 9,500, which confirms that the percentage is consistent with the target. Why Other Options Are Wrong: - 11 9/22 percent and 8 9/22 percent: These values are too small and do not produce an increase of 9,500 cars when applied to 41,800. - 8 11/23 percent: This is also too low and does not match the calculated fraction 95 / 418. Common Pitfalls: One frequent mistake is to divide the increase by the new target instead of by the original value, which would underestimate the required growth. Another is rounding too early, which can slightly change the fraction and make it hard to match the provided options. Always compute the increase first, then divide by the original base value, and only then convert the result carefully into a fraction or mixed number. Final Answer: The sales must be increased by 22 8/11 percent to reach the new target.

Question 11

The list price of a television set is 2,300 rupees and it is sold with two successive discounts of 25 percent and 10 percent. What is the final selling price of the television set?

Accepted Answer

Introduction / Context: This percentage question deals with successive discounts on a marked or list price. Such questions often appear in shopping, commerce, and competitive exams. The key is to understand that successive discounts are applied one after another on the reduced price, not added directly as a single percentage on the original price. Given Data / Assumptions: - List price of the television = 2,300 rupees. - First discount = 25 percent on the list price. - Second discount = 10 percent on the already reduced price. - We need the final selling price after both discounts. Concept / Approach: When two discounts are given successively, the second discount is not on the original price but on the price obtained after the first discount. Therefore, the effective multiplication factor is (1 - first discount) multiplied by (1 - second discount). We can compute each step separately or directly use the product of the remaining percentages to find the final price. Step-by-Step Solution: Step 1: First discount is 25 percent, so the price after the first discount is 75 percent of 2,300.Step 2: Compute 75 percent of 2,300: 0.75 * 2,300 = 1,725 rupees.Step 3: Second discount is 10 percent on 1,725, so the customer pays 90 percent of 1,725.Step 4: Compute 90 percent of 1,725: 0.90 * 1,725 = 1,552.5 rupees.Step 5: Therefore the selling price after both discounts is 1,552.5 rupees. Verification / Alternative check: An alternative is to compute the combined multiplicative factor in one step. After a 25 percent discount you pay 0.75 of the list price, and after a further 10 percent discount you pay 0.90 of that reduced price. So the net factor is 0.75 * 0.90 = 0.675. Then 0.675 * 2,300 = 1,552.5 rupees, which matches the earlier calculation, confirming the answer. Why Other Options Are Wrong: - 1,255.5 rupees and 1,525.5 rupees are too low and result from misapplying or compounding discounts incorrectly. - 1,555.2 rupees is close but not exact and may result from a rounding or multiplication error. The exact computation leads to 1,552.5 rupees. Common Pitfalls: Many learners incorrectly add discounts directly, for example treating 25 percent plus 10 percent as a single 35 percent discount on the list price. This is wrong because the second discount is applied to a smaller base, not to the original amount. Another common mistake is doing percentage calculations with incorrect factors or rounding too early. Always convert discounts to their fractional or decimal equivalents and carefully apply them step by step. Final Answer: The final selling price of the television set is 1,552.5 rupees.

Question 12

If the salary of person A is 40 percent less than the salary of person B, then by what percentage is the salary of B greater than the salary of A?

Accepted Answer

Introduction / Context: This problem explores forward and reverse percentage changes, a very important concept for salary comparisons, price changes, and profit and loss questions. It is easy to say that one value is 40 percent less than another, but the reverse comparison (how much greater the larger value is than the smaller) does not use the same percentage. Given Data / Assumptions: - Let the salary of B be some convenient base value, say 100 units. - A has 40 percent less salary than B. - Therefore, salary of A is 60 percent of salary of B. - We need the percentage by which salary of B is greater than salary of A. Concept / Approach: When one quantity is a certain percent less than another, the reverse comparison uses a different percentage because the base changes. We treat B as 100 units, compute A as 60 units, and then ask what percentage 40 units represents when compared to the smaller base of 60 units. The ratio of the difference to the smaller value gives the required percentage. Step-by-Step Solution: Step 1: Assume salary of B = 100 units.Step 2: A has 40 percent less than B, so salary of A = 100 - 40 = 60 units.Step 3: The difference between B and A is 100 - 60 = 40 units.Step 4: We need how much greater 100 is compared to 60, expressed as a percentage of 60.Step 5: Required percentage = (Difference / Salary of A) * 100 = (40 / 60) * 100.Step 6: Simplify 40 / 60 = 2 / 3, so percentage = (2 / 3) * 100 = 66 2/3 percent. Verification / Alternative check: Another way is to use algebra. Let salary of A be x and salary of B be y. Given that x = 0.6 * y. Then y = x / 0.6. The increase from x to y is y - x = x / 0.6 - x = (x - 0.6 * x) / 0.6 = 0.4 * x / 0.6 = (2 / 3) * x. Percentage increase = (Increase / x) * 100 = (2 / 3) * 100 = 66 2/3 percent, confirming the earlier result. Why Other Options Are Wrong: - 33 1/3 percent and 33 2/3 percent are based on confusing the percentage of reduction with the reverse comparison. - 66 1/3 percent is close but numerically incorrect; the exact value is 66 2/3 percent. Common Pitfalls: A very common error is to think that if A is 40 percent less than B, then B must be 40 percent more than A. This is not correct because the base values are different in each comparison. Another mistake is not choosing a convenient base value like 100 units, which makes the arithmetic clearer. Always rebase the percentage when reversing the direction of comparison. Final Answer: The salary of B is 66 2/3 percent more than the salary of A.

Question 13

If the selling price of an item is 1,000 rupees after giving a discount of 20 percent on the marked price, then what was the original marked price of the item?

Accepted Answer

Introduction / Context: This question is a straightforward application of percentage discount and reverse calculation of marked price from a known selling price. Such problems frequently appear in profit and loss sections of aptitude tests and help reinforce the relationship between marked price, discount, and selling price. Given Data / Assumptions: - Let the marked price be M rupees. - A discount of 20 percent is offered on the marked price. - The resulting selling price is 1,000 rupees. - We need to find the value of M. Concept / Approach: A discount of 20 percent means the customer pays 80 percent of the marked price. Therefore the selling price equals 80 percent of M. We can express this as an equation, solve for M, and find the original marked price. Working with decimal factors is usually simpler than repeatedly manipulating percentages. Step-by-Step Solution: Step 1: After a 20 percent discount, the buyer pays 100 percent - 20 percent = 80 percent of M.Step 2: In decimal form, 80 percent = 0.8.Step 3: Therefore, selling price SP = 0.8 * M.Step 4: Given SP = 1,000 rupees, we have 0.8 * M = 1,000.Step 5: Solve for M: M = 1,000 / 0.8.Step 6: Compute 1,000 / 0.8 = 1,250 rupees.So, the marked price of the item was 1,250 rupees. Verification / Alternative check: Verify by applying the discount to the found marked price. Take 20 percent of 1,250, which is 0.2 * 1,250 = 250 rupees. Subtract this discount from the marked price: 1,250 - 250 = 1,000 rupees. This equals the given selling price, so the solution is consistent. Why Other Options Are Wrong: - 1,200 rupees and 1,400 rupees do not produce a selling price of exactly 1,000 rupees when reduced by 20 percent. - 800 rupees is less than the selling price itself, which is impossible when a discount is applied; the selling price must always be less than or equal to the marked price in a normal discount situation. Common Pitfalls: A common mistake is to subtract 20 percent of 1,000 from 1,000, wrongly assuming the selling price is the base for the discount. The discount is always calculated on the marked price, not the final price. Another error is to treat 20 percent as 0.2 and add instead of subtract, or to forget to reverse the operation when solving for the original value. Always set up a clear equation that links selling price, discount percent, and marked price. Final Answer: The original marked price of the item was 1,250 rupees.

Question 14

Twenty is 0.25 percent of which number?

Accepted Answer

Introduction / Context: This question checks comfort with very small percentages by asking you to reverse the usual operation. Instead of finding a percentage of a number, you are given the result and asked to recover the original number. Such reverse percentage problems are common in aptitude exams and strengthen your understanding of percentage as a fraction of 100. Given Data / Assumptions: - Let the unknown number be N. - 0.25 percent of N equals 20. - 0.25 percent means 0.25 out of 100. - We need to find the value of N that satisfies this relationship. Concept / Approach: Percent literally means "per hundred". So 0.25 percent of N is (0.25 / 100) * N. The equation (0.25 / 100) * N = 20 can be solved to find N. It is often convenient to convert 0.25 percent to its decimal form 0.0025 and then divide the given value by this factor to obtain the original number. Step-by-Step Solution: Step 1: Express 0.25 percent as a decimal factor. 0.25 percent = 0.25 / 100 = 0.0025.Step 2: Write the relationship: 0.0025 * N = 20.Step 3: Solve for N by dividing both sides by 0.0025.Step 4: N = 20 / 0.0025.Step 5: Compute 20 / 0.0025. Since 0.0025 = 25 / 10,000, dividing 20 by 0.0025 gives 20 * (10,000 / 25) = 20 * 400 = 8,000.Step 6: Therefore N = 8,000. Verification / Alternative check: Check by computing 0.25 percent of 8,000 directly. First find 1 percent of 8,000, which is 80. Then 0.25 percent is one quarter of 1 percent, so it is 80 / 4 = 20. This matches the given result, confirming that the original number is 8,000. Why Other Options Are Wrong: - 10,000 would give 0.25 percent of 10,000 as 25, not 20. - 5,000 would give 0.25 percent as 12.5, which is too small. - 2,500 would give 0.25 percent as 6.25, which is even smaller and clearly does not match 20. Common Pitfalls: Students sometimes confuse 0.25 percent with 25 percent, which is a hundred times larger. Another mistake is to divide 20 by 0.25 instead of by 0.25 percent, forgetting to divide by 100 as well. Always convert the given percentage correctly into a decimal or fractional factor before forming the equation. Final Answer: The required number is 8,000.

Question 15

If one saree is offered free on the purchase of three sarees at the same marked price, what is the effective discount percentage on each saree?

Accepted Answer

Introduction / Context: Shops often use "buy one, get one free" type offers instead of directly saying a percentage discount. This question asks you to translate an offer of one free saree on the purchase of three sarees into an equivalent percentage discount on each saree. Understanding this helps in comparing different promotional schemes in real life and in exams. Given Data / Assumptions: - All sarees have the same marked price; call it P rupees per saree. - The customer buys 3 sarees and gets 1 saree free. - Total sarees received = 4. - Total amount paid = price of 3 sarees = 3P. - We want the effective discount percentage compared to paying full price for all 4 sarees. Concept / Approach: If there were no offer, the customer would pay full price for all 4 sarees, that is 4P rupees. With the offer, the customer still receives 4 sarees but pays only 3P rupees. The difference 4P - 3P equals the discount amount. The effective discount percentage is then the discount divided by the original full price, multiplied by 100. Step-by-Step Solution: Step 1: Full price without offer for 4 sarees = 4P rupees.Step 2: Price actually paid with the offer = 3P rupees.Step 3: Discount amount = 4P - 3P = P rupees.Step 4: Effective discount percentage = (Discount / Full price) * 100.Step 5: Substitute values: Effective discount percentage = (P / 4P) * 100.Step 6: Simplify P / 4P = 1 / 4.Step 7: Therefore, effective discount percentage = (1 / 4) * 100 = 25 percent. Verification / Alternative check: Assume a numerical value for P, say P = 100 rupees. Then without offer, 4 sarees would cost 400 rupees. With the offer, you pay 300 rupees for 4 sarees. The discount is 100 rupees. Discount percentage = (100 / 400) * 100 = 25 percent. This agrees with the general algebraic solution. Why Other Options Are Wrong: - 20 percent and 30 percent do not match the exact ratio of 1 free out of 4 total sarees. - 40 percent would mean a much larger price reduction; that would correspond to paying only 60 percent of the total, which is not the case here since the customer pays 3 out of 4 parts, that is 75 percent of the total. Common Pitfalls: Some learners mistakenly compute the discount as 1 out of 3 and say 33.33 percent, forgetting that the correct base is the total value of 4 sarees, not just the paid ones. Always compare the discount value to the full price of the goods received. Thinking in terms of "total cost without offer" versus "actual cost with offer" usually clarifies the correct base for the percentage calculation. Final Answer: The effective discount on each saree is 25 percent.

Question 16

The discount offered on a shirt with marked price 500 rupees is 20 percent, and the discount on a pair of trousers with marked price 1,000 rupees is 40 percent. If Ajay buys 2 shirts and 3 pairs of trousers, what is the effective overall discount pe…

Accepted Answer

Introduction / Context: This is a mixed discount problem where different items have different discount rates. The goal is to find the effective discount percentage on the total bill. Such questions mimic real shopping situations and require careful calculation of total marked price and total amount paid before computing the single equivalent discount percentage. Given Data / Assumptions: - Marked price of one shirt = 500 rupees, discount on shirts = 20 percent. - Marked price of one pair of trousers = 1,000 rupees, discount on trousers = 40 percent. - Ajay buys 2 shirts and 3 pairs of trousers. - We must find the overall effective discount percentage on the combined purchase. Concept / Approach: First calculate the total marked price of all items. Then apply the respective discounts to each category to get the actual amount paid. The difference between total marked price and total amount paid gives the total discount. Finally, the effective discount percentage is total discount divided by total marked price, times 100. Step-by-Step Solution: Step 1: Total marked price of shirts = 2 * 500 = 1,000 rupees.Step 2: Total marked price of trousers = 3 * 1,000 = 3,000 rupees.Step 3: Overall marked price = 1,000 + 3,000 = 4,000 rupees.Step 4: Discount on shirts = 20 percent of 1,000 = 0.20 * 1,000 = 200 rupees; so Ajay pays 800 rupees for shirts.Step 5: Discount on trousers = 40 percent of 3,000 = 0.40 * 3,000 = 1,200 rupees; so Ajay pays 1,800 rupees for trousers.Step 6: Total amount paid = 800 + 1,800 = 2,600 rupees.Step 7: Total discount = Total marked price - Total amount paid = 4,000 - 2,600 = 1,400 rupees.Step 8: Effective discount percentage = (1,400 / 4,000) * 100 = 35 percent. Verification / Alternative check: You can also think in terms of weighted average discount rates. Shirts contribute 1,000 out of 4,000 of the marked price and have 20 percent discount; trousers contribute 3,000 out of 4,000 and have 40 percent discount. Weighted discount = (1,000 / 4,000) * 20 + (3,000 / 4,000) * 40 = 0.25 * 20 + 0.75 * 40 = 5 + 30 = 35 percent. This matches the earlier calculation. Why Other Options Are Wrong: - 30 percent and 32 percent underestimate the savings and do not match the actual discount amount of 1,400 rupees. - 25 percent is far too low and would correspond to a discount of only 1,000 rupees on 4,000 rupees of goods. Common Pitfalls: Some students mistakenly average the two discount percentages directly, for example (20 percent + 40 percent) / 2 = 30 percent, without considering that the total marked price spent on each category is different. The correct approach is to use actual rupee values or a weighted average based on total marked price contributions. Always compute total marked price, total amount paid, and then derive the effective percentage from these totals. Final Answer: The effective overall discount percentage Ajay receives is 35 percent.

Question 17

A man wills 40 percent of his wealth to his wife and the remaining 60 percent to his children. The wealth received by the children is what percentage of the wealth willed to the wife?

Accepted Answer

Introduction / Context: This is a ratio and percentage comparison question. It asks you to compare the share of one group (children) to the share of another group (wife) in terms of percentage. Problems like this are common in profit sharing, inheritance, and partnership distributions. Given Data / Assumptions: - Total wealth is assumed to be 100 units for simplicity. - Wife receives 40 percent of the wealth, so her share = 40 units. - Children together receive the remaining 60 percent, so their share = 60 units. - We must express the children's share as a percentage of the wife's share. Concept / Approach: To express one quantity as a percentage of another, divide the first quantity by the second and multiply by 100. Here, the children's share must be divided by the wife's share and then expressed as a percentage. Using a base total of 100 makes the arithmetic very straightforward and preserves all ratios. Step-by-Step Solution: Step 1: Assume total wealth = 100 units.Step 2: Wife's share = 40 percent of 100 = 40 units.Step 3: Children's combined share = 100 - 40 = 60 units.Step 4: To find percentage of wife's share represented by children's share, compute (Children's share / Wife's share) * 100.Step 5: Substitute values: (60 / 40) * 100.Step 6: Simplify 60 / 40 = 3 / 2 = 1.5.Step 7: Therefore, percentage = 1.5 * 100 = 150 percent. Verification / Alternative check: You can also think of it as a ratio. The wife:children ratio is 40:60, which simplifies to 2:3. This means children's share is 1.5 times the wife's share. A quantity that is 1.5 times another is 150 percent of it, because 1.5 equals 150 percent when written as a percentage. This matches the algebraic method. Why Other Options Are Wrong: - 66.6 percent and 50 percent correspond to reverse or incorrect comparisons; they do not represent how much greater 60 is relative to 40. - 20 percent is far too small and would mean the children receive much less than the wife, which contradicts the given division of 40 percent and 60 percent. Common Pitfalls: A typical confusion is mixing up "percentage of total wealth" with "percentage of another person's share." The children receive 60 percent of total wealth, not 60 percent more than the wife. Another error is comparing the wife's share to the children's share instead of the other way around, which would lead to 66.6 percent. Always check which quantity needs to be expressed as a percentage of which base. Final Answer: The children receive 150 percent of the wealth willed to the wife.

Question 18

At a 20 percent discount the selling price of an article is 2,400 rupees. What will be the selling price of the same article if the discount is increased to 32.5 percent?

Accepted Answer

Introduction / Context: This question combines forward and reverse percentage calculations involving discounts. First, you must recover the marked price from a known selling price at one discount rate, and then use the same marked price to compute a new selling price at a different discount rate. This kind of multi step thinking is very common in profit and loss aptitude questions. Given Data / Assumptions: - At 20 percent discount, selling price (SP1) = 2,400 rupees. - Discount is given on marked price (M). - We must first find M, then apply a discount of 32.5 percent to find new selling price (SP2). Concept / Approach: When a discount of d percent is applied, the customer pays (100 - d) percent of the marked price. So SP1 = (1 - 0.20) * M = 0.80 * M. After finding M from this equation, we apply the second discount of 32.5 percent, so SP2 = (1 - 0.325) * M = 0.675 * M. Working with decimal multipliers makes the steps straightforward. Step-by-Step Solution: Step 1: 20 percent discount means the customer pays 80 percent, or 0.80, of the marked price.Step 2: Given SP1 = 2,400 rupees, we have 0.80 * M = 2,400.Step 3: Solve for M: M = 2,400 / 0.80 = 3,000 rupees.Step 4: Now the discount is 32.5 percent, so the customer pays 100 percent - 32.5 percent = 67.5 percent of M.Step 5: In decimal form, 67.5 percent = 0.675.Step 6: New selling price SP2 = 0.675 * 3,000.Step 7: Compute SP2: 0.675 * 3,000 = 2,025 rupees. Verification / Alternative check: Check the logic by reversing. If marked price is 3,000 rupees, then at 20 percent discount, the price is 0.80 * 3,000 = 2,400, which matches the given condition. At 32.5 percent discount, the amount of discount is 0.325 * 3,000 = 975 rupees. Subtracting this from 3,000 gives 3,000 - 975 = 2,025 rupees, agreeing with the earlier calculation. Why Other Options Are Wrong: - 2,125 and 2,225 rupees correspond to smaller discounts than 32.5 percent on a 3,000 rupee article. - 2,325 rupees is closer to the original selling price at 20 percent discount and does not reflect the larger discount of 32.5 percent. Common Pitfalls: One frequent mistake is to apply the new discount directly on the old selling price of 2,400 rupees instead of on the marked price. Discounts always apply to the marked price, not to the previous selling price. Another error is to add or subtract percentages directly without converting them into multiplicative factors on the marked price. Final Answer: The new selling price at a 32.5 percent discount is 2,025 rupees.

Question 19

After excluding stoppages, the speed of a bus is 60 km/h, but including stoppages its average speed falls to 45 km/h. For how many minutes per hour does the bus stop?

Accepted Answer

Introduction / Context: This question combines average speed with the idea of stoppage time. It tests whether you understand how halts affect the effective average speed of a vehicle and how to convert between hours and minutes while handling distances. The concept appears often in time, speed, and distance sections of aptitude exams. Given Data / Assumptions: - Actual running speed when the bus is moving = 60 km/h. - Average speed including stoppages = 45 km/h. - Time considered = 1 hour of clock time (for convenience). - Let running time in that hour be t hours and stoppage time be s hours, with t + s = 1. - Distance covered in the hour is 45 km (since average speed is 45 km/h for 1 hour). Concept / Approach: If we know the effective average speed over one hour, we can find the distance covered in that hour. That distance must also equal the running speed multiplied by the actual running time, because no distance is covered during stoppages. By equating 60 * t to 45, we can find t. Then, stoppage time s is simply 1 - t. Finally, convert s from hours into minutes. Step-by-Step Solution: Step 1: Distance covered in one hour of clock time at an average of 45 km/h is 45 km.Step 2: Let the bus actually runs for t hours at 60 km/h during this period.Step 3: Distance covered while running = 60 * t km.Step 4: This distance must equal 45 km, so 60 * t = 45.Step 5: Solve for t: t = 45 / 60 = 3 / 4 hours.Step 6: Stoppage time per hour s = 1 - t = 1 - 3 / 4 = 1 / 4 hour.Step 7: Convert 1 / 4 hour to minutes: (1 / 4) * 60 = 15 minutes. Verification / Alternative check: Check by recomputing the average speed from these times. In one hour, the bus runs for 45 minutes at 60 km/h. Distance covered = 60 * (45 / 60) = 45 km. Average speed = total distance / total time = 45 km / 1 hour = 45 km/h, which matches the given information. Therefore 15 minutes stoppage per hour is consistent. Why Other Options Are Wrong: - 10, 9, and 12 minutes would correspond to different effective average speeds; substituting them into the calculation would not yield 45 km/h as the combined average speed. Common Pitfalls: Some students incorrectly assume that average speed is the arithmetic mean of 60 km/h and 0, which would be 30 km/h, not 45 km/h. Another mistake is to forget that average speed equals total distance divided by total time, not simply an average of speeds. Also, ensure that you use the same time unit (hours or minutes) consistently in the calculation and only convert at the end. Final Answer: The bus stops for 15 minutes in every hour.

Question 20

If a shopkeeper sells an item for 4,400 rupees when its marked price is 5,000 rupees, then what percentage discount is he offering?

Accepted Answer

Introduction / Context: This standard profit and loss question asks you to calculate the discount percentage when both marked price and selling price are known. Such problems help you practice the basic relationship between marked price, discount amount, and discount rate, which is essential for commercial arithmetic. Given Data / Assumptions: - Marked price (MP) = 5,000 rupees. - Selling price (SP) = 4,400 rupees. - Discount amount = MP - SP. - Discount percentage = (Discount amount / MP) * 100 percent. Concept / Approach: The discount amount is the reduction from the marked price. Once we compute the rupee discount, we express that amount as a fraction of the marked price and then convert it into a percentage by multiplying by 100. It is important to remember that the base for discount percentage is always the marked price, not the selling price or cost price. Step-by-Step Solution: Step 1: Compute the discount amount: Discount = MP - SP = 5,000 - 4,400.Step 2: Discount amount = 600 rupees.Step 3: Use the formula: Discount percentage = (Discount / MP) * 100.Step 4: Substitute values: Discount percentage = (600 / 5,000) * 100.Step 5: Simplify 600 / 5,000 = 0.12.Step 6: So discount percentage = 0.12 * 100 = 12 percent. Verification / Alternative check: Another way is to see that 10 percent of 5,000 is 500 rupees. The discount here is 600 rupees, which is 100 rupees more than 10 percent, and 100 rupees is 2 percent of 5,000. Therefore the total discount of 600 rupees is 12 percent of the marked price (10 percent plus 2 percent), confirming the result. Why Other Options Are Wrong: - 20 percent and 15 percent represent larger discounts than 600 rupees on a 5,000 rupee item; 20 percent would be 1,000 rupees off and 15 percent would be 750 rupees off. - 10 percent corresponds to a 500 rupee discount, which is smaller than the actual discount of 600 rupees. Common Pitfalls: One common mistake is to use the selling price as the base when computing the discount percentage, which would give (600 / 4,400) * 100 and an incorrect value. Always use the marked price as the denominator when dealing with discount percentages. Another error is subtracting percentages instead of actual rupee amounts, which does not apply here because only one discount is given. Final Answer: The discount offered by the shopkeeper is 12 percent.

Percentage Questions