Question 1

Tickets for an adult cost Rs 1600 and for a child cost Rs 600. Under a special offer, 1 child ticket is given free with every 2 adult tickets. If a group has 17 adults and 7 children, what discount percentage does the group effectively receive on th…

Accepted Answer

Introduction / Context: This question combines ticket pricing with a promotional offer that gives free child tickets when a certain number of adult tickets are purchased. You must compare the cost without the offer to the cost with the offer to find the overall discount percentage. Such problems test your ability to handle grouped offers and percentage discount calculations. Given Data / Assumptions: Price of one adult ticket = Rs 1600. Price of one child ticket = Rs 600. Offer: 1 child ticket free for every 2 adult tickets purchased. Group size: 17 adults and 7 children. We assume the offer is applied in the most beneficial way for the group. Concept / Approach: First, compute the total amount the group would pay if there were no offer at all. Then, apply the offer to determine how many child tickets will be free based on the number of adult tickets. Compute the actual amount paid under the offer. The discount is the difference between the no-offer cost and the offer cost. The discount percentage is calculated relative to the no-offer cost. Step-by-Step Solution: Without any offer, cost for 17 adults = 17 * 1600 = 27200.Without any offer, cost for 7 children = 7 * 600 = 4200.Total cost without offer = 27200 + 4200 = 31400.Under the offer, for every 2 adults, 1 child goes free.Number of adult pairs in 17 adults = floor(17 / 2) = 8 pairs, leaving 1 extra adult.Each pair can get 1 child free, so up to 8 children can be free, but there are only 7 children.So all 7 children can get free tickets.Under the offer, the group pays only for adult tickets: 17 * 1600 = 27200.Discount amount = 31400 − 27200 = 4200.Discount percentage = (4200 / 31400) * 100 ≈ 13.37%. Verification / Alternative check: Compute the fraction 4200 / 31400. Dividing numerator and denominator by 100 gives 42 / 314. This is approximately 0.1337. Multiply by 100 to get 13.37%. This matches the option given and confirms that the discount percentage has been calculated correctly. Why Other Options Are Wrong: 26.02% and 24.41%: These values are much larger and would correspond to a significantly lower payment compared to the original cost, which does not match the calculation. 32.2%: This would imply that nearly one third of the total fare is saved, which is inconsistent with only 7 child tickets being free. 20%: This is a rough guess and does not match the exact ratio 4200 / 31400. Common Pitfalls: Some students miscount the number of free child tickets by taking 17 / 2 as 8.5 and then using 8 or 9 incorrectly. Others may assume only 16 adults count and ignore the extra adult, leading to misapplication of the offer. A further mistake is to compute discount percentage based on the amount paid instead of the original total cost. Always base the percentage discount on the full no-offer amount. Final Answer: The group effectively receives a discount of about 13.37%.

Question 2

A retailer offers a discount of 20% on the marked price of goods and, as a result, sells them exactly at cost price. What was the percentage mark up of the marked price over the cost price?

Accepted Answer

Introduction / Context: This problem relates discount percentage to mark up percentage. The retailer marks the goods above cost price, then gives a discount and still ends up selling at cost price. You are asked to compute how much the goods were marked up initially. This is a classic application of percentage change in pricing. Given Data / Assumptions: Let cost price of the item be C. Marked price of the item is some percentage above C. A discount of 20% on the marked price is allowed. After this discount, the selling price equals the cost price C. We need to find the percentage mark up from C to the marked price. Concept / Approach: When the retailer gives a discount of 20% on the marked price M, the selling price becomes 80% of M. The question states that this selling price equals the cost price C. So 80% of M is equal to C. From this equation, we can express M in terms of C and then find what percentage M is above C. The mark up percentage is (M − C) / C * 100. Step-by-Step Solution: Let cost price be C and marked price be M.A 20% discount on M means the selling price is 80% of M = 0.80 * M.Given that selling price equals cost price C.So 0.80 * M = C.Rearrange: M = C / 0.80.Compute M: C / 0.80 = 1.25 * C.Mark up amount = M − C = 1.25C − C = 0.25C.Mark up percentage = (0.25C / C) * 100 = 25%. Verification / Alternative check: Assume a simple cost price, say C = Rs 100. Then marked price M = 1.25 * 100 = Rs 125. With a 20% discount on Rs 125, the reduction is 20% of 125 = 25. Selling price becomes 125 − 25 = Rs 100, which is exactly the cost price. This confirms that a 25% mark up combined with a 20% discount leads to a break-even sale. Why Other Options Are Wrong: 20%: A 20% mark up would make M = 1.20C. After a 20% discount, selling price would be 80% of 1.20C = 0.96C, which is below cost price. 30% and 40%: These would lead to M = 1.30C or 1.40C, and after a 20% discount, the selling price would be above cost price, resulting in profit rather than break-even. 15%: This mark up is too low and would result in a loss after a 20% discount. Common Pitfalls: Some learners confuse the mark up percentage with the discount percentage and assume they must be the same. Others forget that the discount is applied on the marked price, not on the cost price. It is important to carefully define variables, translate the given conditions into equations, and then solve step by step. Final Answer: The retailer marked up the goods by 25% over the cost price.

Question 3

The population of a town increases by 5% in the first year, by 6% in the second year, and by 8% in the third year. If the present population after these three increases is 120204, what was the population of the town 3 years ago?

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Introduction / Context: This question is a classic example of successive percentage increase applied to population growth. The population grows by different percentages each year. The final population is given and the task is to compute the population at the beginning of the three-year period. This is essentially a reverse successive percentage problem, similar to compound growth in finance. Given Data / Assumptions: First year increase: 5%. Second year increase: 6%. Third year increase: 8%. Population after three years = 120204. We assume growth is applied sequentially on the latest population each year. Concept / Approach: Each yearly increase can be represented as a multiplication factor: 5% increase corresponds to a factor 1.05, 6% to 1.06, and 8% to 1.08. The total growth factor over three years is the product of these three factors. Let the initial population be P. Then P multiplied by the total growth factor equals the final population 120204. We then divide the final population by this growth factor to find P. Step-by-Step Solution: Let the population 3 years ago be P.After first year with 5% growth, population = P * 1.05.After second year with 6% growth, population = P * 1.05 * 1.06.After third year with 8% growth, population = P * 1.05 * 1.06 * 1.08.Total growth factor = 1.05 * 1.06 * 1.08.Compute 1.05 * 1.06 = 1.113.Then 1.113 * 1.08 = 1.20204.So final population = P * 1.20204 = 120204.Therefore, P = 120204 / 1.20204 = 100000. Verification / Alternative check: Verify by forward computation using P = 100000. After first year: 100000 * 1.05 = 105000. After second year: 105000 * 1.06 = 111300. After third year: 111300 * 1.08 = 120204. The computed final population matches the given value exactly, confirming that the original population was 100000. Why Other Options Are Wrong: 102000 and 101204: These values, when grown by 5%, 6%, and 8%, do not reach exactly 120204. 98000: This would produce a significantly smaller final population after three years. 105000: This is actually the population after the first 5% increase, not at the beginning of the period. Common Pitfalls: A common mistake is to add the percentages (5 + 6 + 8 = 19%) and treat it as a single increase of 19%, which is incorrect because percentage increases compound multiplicatively, not additively. Another error is to treat the final population as if it were obtained by simple interest, dividing repeatedly without using growth factors. Always express each increase as a multiplication factor and multiply them to get the overall factor. Final Answer: The population of the town 3 years ago was 100000.

Question 4

Hiten marks a pen at Rs 9800. After allowing a discount of 20% on this marked price, he still makes a profit of 12%. What is the cost price of the pen in rupees?

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Introduction / Context: This question combines concepts of marked price, discount, and profit. Hiten marks the pen above cost price, gives a discount, and still earns a profit. You are required to find the original cost price. This is a typical profit and loss problem that requires careful percentage handling. Given Data / Assumptions: Marked price M = Rs 9800. Discount allowed = 20% on marked price. After discount, Hiten earns a profit of 12% on cost price. We must determine the cost price C. Concept / Approach: First, we use the discount percentage to compute the selling price as a fraction of the marked price. Then we use the profit percentage to express the selling price in terms of cost price. Since both expressions refer to the same selling price, we equate them and solve for cost price. This approach ties together discount and profit percentages clearly. Step-by-Step Solution: Marked price M = Rs 9800.Discount = 20%, so selling price is 80% of marked price.Selling price SP = 0.80 * 9800 = 7840.Profit = 12% on cost price, so SP = 112% of C = 1.12 * C.Therefore, 1.12 * C = 7840.So C = 7840 / 1.12.Compute C: 7840 / 1.12 = 7000. Verification / Alternative check: Verify the result by forward calculation. If cost price is Rs 7000, a 12% profit means selling price should be 1.12 * 7000 = Rs 7840. With a 20% discount on a marked price of Rs 9800, selling price is 80% of 9800, which is also Rs 7840. Both conditions agree, confirming that the cost price is indeed Rs 7000. Why Other Options Are Wrong: 7600 and 7200: If either were taken as cost price, the 12% profit would give a selling price that does not match the discounted price from 9800. 6500 and 6800: These are too low and lead to larger profit percentages than 12% when combined with the given discounted selling price. Common Pitfalls: Students sometimes apply the discount to the cost price instead of the marked price, which changes the whole structure of the problem. Another frequent error is adding or subtracting percentage values directly without converting them to their proper roles (discount on marked price, profit on cost price). Clearly label each quantity and write equations for selling price in two ways to avoid confusion. Final Answer: The cost price of the pen is Rs 7000.

Question 5

Tickets for an adult cost Rs 1500 and for a child cost Rs 800. Under an offer, 1 child goes free with every 2 adults. If a group has 25 adults and 12 children, what discount percentage does the group effectively receive on the total ticket cost?

Accepted Answer

Introduction / Context: This question again explores a ticket discount scheme where a child ticket is free for every two adult tickets purchased. You must compute the group's overall discount percentage by comparing the cost with and without the offer. It reinforces understanding of grouped offers and effective discount calculations. Given Data / Assumptions: Price of one adult ticket = Rs 1500. Price of one child ticket = Rs 800. Offer: 1 child free with every 2 adult tickets. Group size: 25 adults and 12 children. The offer is applied as many times as possible, benefiting the group optimally. Concept / Approach: We first compute the total amount the group would pay in the absence of any offer. Then we apply the offer to find how many child tickets are free based on the number of adult tickets. We find the actual amount paid under the scheme and then determine the discount percentage relative to the original total cost. Step-by-Step Solution: Without any offer, cost for 25 adults = 25 * 1500 = 37500.Without any offer, cost for 12 children = 12 * 800 = 9600.Total cost without offer = 37500 + 9600 = 47100.Under the offer, for every 2 adults, 1 child goes free.Number of adult pairs in 25 adults = floor(25 / 2) = 12 pairs, with 1 adult left over.There are 12 children, so all 12 children can be free under the offer.Thus, the group pays only for adult tickets: 25 * 1500 = 37500.Discount amount = 47100 − 37500 = 9600.Discount percentage = (9600 / 47100) * 100.Compute 9600 / 47100 ≈ 0.2038, so discount percentage ≈ 20.38%. Verification / Alternative check: The fraction 9600 / 47100 can be simplified by dividing numerator and denominator by 100 to 96 / 471. Approximating 96 / 471 gives approximately 0.2038. Multiplying by 100 confirms that the discount percentage is about 20.38%. This matches the option listed and verifies our calculation. Why Other Options Are Wrong: 26.47% and 31.60%: These larger discount percentages would correspond to greater reductions in the total payment than what results from 12 free child tickets. 25% and 33.33%: These are rounder values but do not reflect the exact ratio of 9600 to 47100, and they do not match the computed effective discount. Common Pitfalls: Errors often arise from miscounting how many child tickets can be free. Some may multiply 25 by 1 free child per adult pair and forget to limit by the number of children. Others forget to use the original without-offer total as the base when computing the discount percentage. Carefully track the number of adult pairs, limit free tickets by actual children present, and always calculate discount percentage using the original no-offer cost. Final Answer: The group receives an effective discount of about 20.38%.

Question 6

At a 22% discount, the selling price of a refrigerator is Rs 26000. If instead a 40% discount were offered on the same marked price, what would be the new selling price in rupees?

Accepted Answer

Introduction / Context: This question links two different discount rates applied to the same marked price. You are told the selling price at one discount rate and asked to find the selling price at another discount rate. It tests your ability to reverse from selling price to marked price and then apply a new discount. Given Data / Assumptions: When a 22% discount is given, selling price SP1 = Rs 26000. Discount rate 1 = 22%, so the customer pays 78% of the marked price. Discount rate 2 = 40%, so the customer will pay 60% of the marked price. The marked price remains the same in both scenarios. Concept / Approach: We first express the given selling price in terms of the marked price using the 22% discount. This allows us to find the marked price. Then we apply the 40% discount to that marked price to find the new selling price. The calculations mainly use basic percentage factors (0.78 and 0.60). Step-by-Step Solution: Let the marked price be M.With a 22% discount, the customer pays 78% of M.So 0.78 * M = 26000.Thus M = 26000 / 0.78.Now, for a 40% discount, the customer pays 60% of M.New selling price SP2 = 0.60 * M.Substitute M from the earlier step: SP2 = 0.60 * (26000 / 0.78).Compute 0.60 / 0.78 = 60 / 78 = 10 / 13.So SP2 = (10 / 13) * 26000.26000 / 13 = 2000, so SP2 = 10 * 2000 = 20000. Verification / Alternative check: We can also first find M numerically. M = 26000 / 0.78 approximately equals 33333.33. Then, with a 40% discount, selling price is 60% of this: 0.60 * 33333.33 ≈ 20000. This agrees with the exact fractional calculation, confirming that the new selling price is Rs 20000. Why Other Options Are Wrong: 14640 and 21840: These correspond to applying incorrect discount factors or miscalculating the ratio between 22% and 40% discounts. 12000: This is far below the correct price and would imply an unrealistically huge discount. 26000: This is the selling price at 22% discount, not at 40% discount. Common Pitfalls: Some learners mistakenly think that the new selling price can be found by scaling 26000 directly by the ratio of 60% to 78% without computing the fraction correctly. Others might subtract percentage points incorrectly (for example, thinking 40% is just 18% more discount and roughly adjusting the price). Always go back to the base marked price when changing discount rates. Final Answer: The selling price of the refrigerator at a 40% discount would be Rs 20000.

Question 7

The number 26 is 0.4% of some number. That unknown number is equal to how much?

Accepted Answer

Introduction / Context: This question tests your understanding of reverse percentage calculations. Instead of finding a percentage of a known number, you are given the percentage value (0.4% of a number equals 26) and must find the original number. This type of question is basic but very common in quantitative aptitude tests. Given Data / Assumptions: 0.4% of an unknown number N equals 26. We must determine the value of N. Percentages are interpreted in the usual way: p% = p / 100. Concept / Approach: We translate the statement "26 is 0.4% of N" into an equation. Since 0.4% means 0.4 / 100 or 0.004 as a decimal, the equation becomes 0.004 * N = 26. Solving this equation for N requires dividing 26 by 0.004. This is a straightforward manipulation of percentages and decimals. Step-by-Step Solution: Given: 0.4% of N = 26.Write 0.4% as a decimal: 0.4% = 0.4 / 100 = 0.004.So the equation is 0.004 * N = 26.Solve for N: N = 26 / 0.004.Rewrite 0.004 as 4 / 1000, so 26 / 0.004 = 26 * (1000 / 4).Compute 1000 / 4 = 250, so N = 26 * 250.26 * 250 = (26 * 100) + (26 * 150) = 2600 + 3900 = 6500. Verification / Alternative check: Check by forward percentage calculation. Take N = 6500 and compute 0.4% of 6500. This is (0.4 / 100) * 6500 = 0.004 * 6500 = 26. Since this matches the given value, the computed N is correct. This quick verification step ensures that no decimal or arithmetic errors were made. Why Other Options Are Wrong: 13000: 0.4% of 13000 is 52, which is double the required value. 650: 0.4% of 650 is 2.6, which is much smaller than 26. 16250 and 10000: For these values, 0.4% gives numbers that are not equal to 26, so they do not satisfy the basic equation. Common Pitfalls: Some students misinterpret 0.4% as 0.4 instead of 0.004, which leads to a very different and incorrect result. Others may try to convert percentages using fractions but mishandle the decimal point. To avoid such mistakes, always remember that p% means p divided by 100, and be careful with decimal place shifts when converting to and from percentages. Final Answer: The required number is 6500.

Question 8

Two successive discounts of 10% and 20% are offered on the marked price of an article. What single equivalent discount percentage would give the same final selling price as these two successive discounts together?

Accepted Answer

Introduction / Context: This aptitude question tests the concept of successive discounts and how to convert them into a single equivalent discount percentage. Many students simply add percentages, which is incorrect when more than one discount is applied one after another. Understanding the correct method is very important for percentage based questions in competitive exams and everyday shopping scenarios. Given Data / Assumptions: First discount = 10% on the marked price. Second discount = 20% on the already discounted price. We assume the same marked price throughout the calculation. We need one single discount that produces the same final selling price. Concept / Approach: The key idea is that successive discounts multiply their remaining price factors. If a discount is d%, the remaining price factor is (1 - d/100). The combined remaining factor of two discounts is the product of the two separate remaining factors. Once this combined factor is known, we compare it with the original price to find the single equivalent discount percentage. Step-by-Step Solution: Step 1: Assume the marked price is 100 units for simplicity.Step 2: After the first discount of 10%, remaining price = 100 * (1 - 10/100) = 100 * 0.9 = 90 units.Step 3: After the second discount of 20% on 90, remaining price = 90 * (1 - 20/100) = 90 * 0.8 = 72 units.Step 4: The final price is 72 units when the marked price was 100 units.Step 5: The single equivalent discount = (100 - 72) percent = 28 percent. Verification / Alternative check: Another way is to work directly with factors. First discount 10% gives factor 0.9. Second discount 20% gives factor 0.8. Combined factor = 0.9 * 0.8 = 0.72. A single discount that leaves 0.72 of the price must be 1 - 0.72 = 0.28 or 28%. This matches our earlier result, so the answer is consistent. Why Other Options Are Wrong: 27% is too small because the remaining price would be 73 units, not 72 units. 25% discount gives a final price of 75 units, which is higher than 72 units, so it is incorrect. 30% discount leaves only 70 units, which is lower than 72 units, so it is not equivalent. 22% is even smaller discount and clearly does not match a final price of 72 units. Common Pitfalls: A very common mistake is to simply add 10% and 20% to get 30%. This ignores the fact that the second discount is not on the original price but on the already reduced price. Another error is to forget to assume a convenient marked price such as 100 units, which makes calculations straightforward. Students should remember that when multiple percentage changes are applied successively, they must be converted into decimal factors, multiplied, and then converted back into a single percentage change. Final Answer: The capacity of a single discount equivalent to successive discounts of 10% and 20% is a discount of 28% on the marked price.

Question 9

The income of A is 25% more than the income of B. B's income is what percentage of A's income?

Accepted Answer

Introduction / Context: This problem checks understanding of percentage increase and how to reverse it to express one quantity as a percentage of another. Many exam questions use relationships between salaries, prices, or marks in exactly this way, so it is important to convert sentences about "more than" or "less than" into simple algebraic expressions. Given Data / Assumptions: Income of A is 25% more than income of B. We need B's income expressed as a percentage of A's income. No actual rupee values are given, so we can assume a convenient value for B. Concept / Approach: When one quantity is a certain percent more than another, we express the larger as a multiple of the smaller. If A is 25% more than B, then A = B * (1 + 25/100) = 1.25 * B. To find B as a percentage of A, we compute B / A and convert that ratio to a percent. Using algebra with assumed values keeps the calculation simple and free from confusion. Step-by-Step Solution: Step 1: Let the income of B be 100 units (this is a convenient assumption).Step 2: Then the income of A is 25% more than 100 units.Step 3: A = 100 * (1 + 25/100) = 100 * 1.25 = 125 units.Step 4: Now compute B as a fraction of A: B / A = 100 / 125.Step 5: Convert this ratio into a percentage: (100 / 125) * 100% = 80%. Verification / Alternative check: Instead of assuming B = 100, we can use algebra. Let B = b. Then A = 1.25 * b. The required percentage is (b / (1.25 * b)) * 100 = (1 / 1.25) * 100. Since 1 / 1.25 = 0.8, the result is 0.8 * 100 = 80%. Both approaches agree, so the result is verified. Why Other Options Are Wrong: 75% would be correct if A was 33.33% more than B, not 25% more, so it does not match the condition here. 50% would mean B has half the income of A, which contradicts A being only 25% higher than B. 25% would suggest B is much smaller compared to A, which is not consistent with the given relation. 60% also does not come from the ratio of 100 to 125 and is simply another distractor value. Common Pitfalls: Candidates often confuse "A is 25% more than B" with "A is 125% of B" and then misinterpret which quantity should be in the numerator when forming the fraction. Another common error is trying to subtract 25 from 100 directly without forming the correct ratio. Always remember that when converting one quantity to a percentage of another, you divide the first by the second and then multiply by 100, keeping the correct order of numerator and denominator. Final Answer: B's income is 80% of A's income.

Question 10

After selling 5% of a certain quantity of sugar, 95 kg of sugar still remains. What was the original quantity of sugar before any part of it was sold?

Accepted Answer

Introduction / Context: This question tests basic percentage application in the context of remaining quantity after a small portion is sold. It is a classic reverse percentage problem where we know what remains and the percentage that this remaining quantity represents of the original stock. Such problems are common in aptitude tests dealing with stock, inventory, and simple commercial arithmetic. Given Data / Assumptions: A shopkeeper sells 5% of a stock of sugar. After this sale, 95 kg of sugar remain. We assume there is no wastage or additional sugar added. We are asked to find the original total quantity of sugar. Concept / Approach: If 5% of the sugar is sold, that means 95% of the original quantity is left. The key idea is to interpret the remaining quantity as a percentage of the original. Once we know that 95 kg represents 95% of the stock, we can set up a simple proportion to find 100% of the stock. This is a straightforward reverse percentage calculation where remaining quantity = percentage factor * original quantity. Step-by-Step Solution: Step 1: Let the original quantity of sugar be Q kg.Step 2: Since 5% is sold, the remaining fraction is 100% - 5% = 95% of Q.Step 3: In decimal form, 95% = 95 / 100 = 0.95.Step 4: We are told that 0.95 * Q = 95 kg.Step 5: Solve for Q: Q = 95 / 0.95 = 100 kg. Verification / Alternative check: Check by forward calculation. If the original quantity is 100 kg, then 5% of 100 kg is 5 kg sold. The remaining sugar is 100 kg - 5 kg = 95 kg. This matches the quantity given in the problem, so the original quantity of 100 kg is confirmed to be correct. Why Other Options Are Wrong: 19 kg would make 95% equal to 19 kg, which is not true, because 5% of 19 kg is 0.95 kg and the remaining amount would be much smaller than 95 kg. 55 kg as 95% would give original 55 / 0.95 = 57.89 kg, but this does not match the structure of the problem and is not among logically expected values. 95 kg would incorrectly assume that there was no sale at all, which contradicts the information about a 5% sale. 75 kg as original amount would leave 0.95 * 75 = 71.25 kg, which is not equal to the specified 95 kg. Common Pitfalls: Many students mistakenly treat the remaining 95 kg as 5% of the original rather than 95%. Others subtract percentages instead of using a simple multiplication and division approach. It is helpful to always convert percentages into decimal factors and to remember that remaining quantity equals percentage remaining times original quantity. Writing the relationship as an equation makes the reasoning clear and avoids mental shortcuts that can lead to errors. Final Answer: The original quantity of sugar was 100 kg.

Question 11

If 21% of an electricity bill is given as a discount, and the remaining amount to be paid is Rs. 1817, what was the original electricity bill before the discount was applied?

Accepted Answer

Introduction / Context: This is a classic reverse percentage question involving a discount on an electricity bill. Instead of asking for the discount itself, the problem gives the discounted payable amount and the discount rate, and asks for the original bill value. Such questions help build confidence in working backward from percentage based changes in billing and commerce situations. Given Data / Assumptions: Discount on the electricity bill = 21% of the original bill. Amount still to be paid after discount = Rs. 1817. The remaining amount represents the portion of the bill after discount. No additional charges or taxes are mentioned, so we ignore them. Concept / Approach: If a discount of d% is given on a bill, then the customer pays (100 - d)% of the original amount. Here, the customer pays 79% of the original bill, because 100% - 21% = 79%. The key idea is to interpret Rs. 1817 as 79% of the original bill. We use a simple proportion equation original * 79 / 100 = 1817, and then solve for the original bill using division. Step-by-Step Solution: Step 1: Let the original bill amount be B rupees.Step 2: Discount is 21% of B, so payable amount = 79% of B.Step 3: Write the relationship as an equation: 0.79 * B = 1817.Step 4: Solve for B: B = 1817 / 0.79.Step 5: Compute the value: B = 2300 rupees, so the original bill was Rs. 2300. Verification / Alternative check: To verify, calculate 21% of Rs. 2300. That gives 2300 * 21 / 100 = 2300 * 0.21 = 483 rupees. Subtract this discount from the original bill: 2300 - 483 = 1817 rupees. This matches the amount stated in the question, so our calculation is confirmed. Why Other Options Are Wrong: Rs. 1502, Rs. 1538 and Rs. 1817 are all less than the payable amount plus discount, so they cannot lead to a payable amount of Rs. 1817 after a 21% reduction. Rs. 2336 would give a payable amount of 79% of 2336, which is 1845.44 rupees, not 1817 rupees, so it is also incorrect. Common Pitfalls: A common mistake is to treat Rs. 1817 as 21% of the bill rather than the remaining 79%, which leads to a very large and incorrect original amount. Another typical error is to subtract 21% of 1817, which is conceptually wrong because the discount applies to the original bill, not to the already discounted amount. Always identify clearly whether the given amount corresponds to the original total, the discounted price, the discount itself, or the remaining part of the quantity. Final Answer: The original electricity bill amount was Rs. 2300.

Question 12

A shopkeeper sells an item for Rs. 1600, while its marked price is Rs. 2000. What percentage discount is the shopkeeper offering on the marked price?

Accepted Answer

Introduction / Context: This question focuses on calculating discount percentage based on marked price and selling price. Understanding how to compute discount percentages is essential for both everyday shopping situations and exam style profit and loss problems. The marked price is the listed price, and the discount is the reduction from this marked price to the selling price. Given Data / Assumptions: Marked price (listed price) of the item = Rs. 2000. Selling price after discount = Rs. 1600. We need to find the discount percentage with respect to the marked price. There are no additional taxes or extra charges mentioned. Concept / Approach: Discount is defined as the difference between marked price and selling price. Discount percentage is calculated as (discount / marked price) * 100. Since all figures are given directly, we only need to compute the difference and express it as a percentage of the marked price. This is a direct application of a basic percentage formula. Step-by-Step Solution: Step 1: Compute the discount amount: discount = marked price - selling price.Step 2: Substitute the values: discount = 2000 - 1600 = 400 rupees.Step 3: Compute the discount percentage using the formula discount percent = (discount / marked price) * 100.Step 4: Substitute the numbers: discount percent = (400 / 2000) * 100.Step 5: Simplify: 400 / 2000 = 0.2, so discount percent = 0.2 * 100 = 20%. Verification / Alternative check: We can also reason mentally. A 10% discount on Rs. 2000 is Rs. 200, so a 20% discount would be twice that, which is Rs. 400. Subtracting Rs. 400 from Rs. 2000 gives Rs. 1600. This matches the given selling price, so a 20% discount is consistent with the information in the question. Why Other Options Are Wrong: 25% discount on Rs. 2000 would be Rs. 500, leading to a selling price of Rs. 1500, not Rs. 1600. 30% discount would be Rs. 600, giving a selling price of Rs. 1400. 10% discount would be only Rs. 200, giving a selling price of Rs. 1800. 15% discount would give Rs. 300 off and a selling price of Rs. 1700. None of these match the given selling price. Common Pitfalls: One frequent mistake is to divide the discount amount by the selling price instead of the marked price. Discount percentages are always calculated on the original or marked price unless explicitly stated otherwise. Another error is misreading the numbers or incorrectly subtracting selling price from marked price. Writing down the formula and substituting values step by step helps avoid these mistakes. Final Answer: The shopkeeper is offering a discount of 20% on the marked price.

Question 13

The price of an article is reduced by 7%. By what percentage must the reduced price be increased so that it returns exactly to the original price?

Accepted Answer

Introduction / Context: This question tests the concept of percentage increase and decrease, especially the important fact that a decrease of a certain percentage does not require the same percentage increase to return to the original value. Instead, the required increase is always slightly higher. This idea appears often in exam questions related to prices, salaries, and population changes. Given Data / Assumptions: An article has an original price which we can call P. The price is cut by 7%. We then need to increase the new reduced price by some percentage so that the price becomes P again. We assume no other changes in price besides this decrease and subsequent increase. Concept / Approach: When a quantity is reduced by d percent, the remaining value is P * (1 - d/100). To restore it to P, we need to find a percentage increase on this reduced value so that the final result equals P. The required percentage increase can be found using the formula: required percent = (d / (100 - d)) * 100, where d is the original percentage decrease. This approach comes directly from equating the increased reduced price to the original price. Step-by-Step Solution: Step 1: Assume the original price P is 100 units for simplicity.Step 2: A decrease of 7% gives new price = 100 * (1 - 7/100) = 100 * 0.93 = 93 units.Step 3: Let the required percentage increase be x% on 93 units.Step 4: After this increase, the price must return to 100 units, so 93 * (1 + x/100) = 100.Step 5: Solve for x: 1 + x/100 = 100 / 93, so x/100 = (100 / 93) - 1.Step 6: Compute x: x = 100 * (100 / 93 - 1) = 100 * (7 / 93) = 700 / 93 ≈ 7.53%. Verification / Alternative check: We can use the standard formula directly: required percent = (d / (100 - d)) * 100. Here d = 7. So required percent = (7 / (100 - 7)) * 100 = (7 / 93) * 100 = 700 / 93 ≈ 7.53%. This matches the detailed step-by-step calculation, confirming the correctness of the result. Why Other Options Are Wrong: 7% is incorrect because an increase of 7% on 93 units only produces 93 * 1.07 = 99.51 units, which does not reach 100. 33.77% and 63.75% are far too high; such large increases would push the value well above the original price. 14% would give 93 * 1.14 = 106.02 units, which is again higher than the original price of 100. Common Pitfalls: The most frequent mistake is assuming that a decrease of 7% can be canceled by an increase of 7%. This is wrong because the base for the increase is the reduced price, not the original price. Another pitfall is applying the formula incorrectly or using the wrong denominator. Students should remember that the denominator in the formula is the remaining percentage after the decrease, which is 100 - d, and not the original percentage. Writing out a simple numerical example with a base of 100 units is often the easiest way to avoid confusion. Final Answer: The reduced price must be increased by approximately 7.53% to restore the original value.

Question 14

An item is sold with a 10% discount on its marked price, and then the customer receives an additional 20% cashback on the amount actually paid. What is the overall effective discount percentage on the marked price?

Accepted Answer

Introduction / Context: This question combines two different benefits: a price discount and a cashback. It checks whether you can track the real amount of money finally spent compared to the marked price. Many online platforms and shopping apps use similar combinations of discounts and cashbacks, so understanding this calculation has both exam and real life value. Given Data / Assumptions: Marked price of the item is assumed to be M. First, a flat discount of 10% is applied on M. After that, the customer receives 20% cashback on the amount paid after the discount. We need the overall effective discount as a percentage of the marked price M. Concept / Approach: The effective discount is based on how much the customer finally spends compared to the marked price. First we calculate the discounted price. Then we calculate the cashback on this discounted amount. Finally, we subtract the cashback from the discounted price to get the net amount actually spent. The effective discount percent is then (marked price - net spend) / marked price * 100. The trick is to perform each step in the correct order and keep track of which amount each percentage applies to. Step-by-Step Solution: Step 1: Assume the marked price M = 100 units for simplicity.Step 2: A 10% discount gives a discounted price of 100 * (1 - 10/100) = 90 units.Step 3: Cashback is 20% of the amount paid, which is 20% of 90 units.Step 4: Cashback = 90 * 20 / 100 = 18 units.Step 5: Net amount paid by the customer = discounted price - cashback = 90 - 18 = 72 units.Step 6: Effective discount = (original marked price - net amount) / original marked price * 100 = (100 - 72) / 100 * 100 = 28 percent. Verification / Alternative check: We can compute in terms of M instead of 100. After a 10% discount, the customer pays 0.9 * M. Cashback is 20% of this, which is 0.2 * 0.9 * M = 0.18 * M. Net payment is 0.9 * M - 0.18 * M = 0.72 * M. Therefore, the customer effectively pays 72% of the marked price. The effective discount is 100% - 72% = 28%. This matches the numeric solution and confirms the result. Why Other Options Are Wrong: 33.6 percent may come from incorrectly adding 10% and 20% of different bases without subtracting properly. 30 percent is a rough guess and does not match the detailed calculation of net payment. 22 percent would correspond to paying 78% of the marked price, which does not arise from the given steps. 18 percent corresponds only to the cashback amount, not the total benefit including the discount. Common Pitfalls: Candidates frequently add 10% and 20% directly to claim a 30% benefit or treat cashback and discount as if both were calculated on the same original base. Another mistake is to forget that cashback is money returned after payment, meaning the effective cost is less than the discounted price. A safe method is always to assume an easy marked price such as 100 units, compute each step in order, and then find the net percentage difference from that original value. Final Answer: The overall effective discount on the marked price is 28 percent.

Question 15

Quantity A is equal to 20% of B, and quantity B is equal to 25% of C. What percentage of C is quantity A?

Accepted Answer

Introduction / Context: This problem checks understanding of chained percentage relationships between three quantities A, B, and C. It is very common in aptitude exams to link variables through percentages and then ask you to express one variable directly as a percentage of another. Mastering this type of question helps in many topics, including ratio, proportion, and basic algebra. Given Data / Assumptions: A is 20% of B. B is 25% of C. We need to find A as a percentage of C. No absolute values are given, so we can comfortably work with symbolic or assumed values. Concept / Approach: Percentages can be converted into fractions or decimal multipliers. A being 20% of B means A = 0.20 * B. B being 25% of C means B = 0.25 * C. By substituting the second relation into the first, we can express A directly in terms of C. Once A is expressed as a decimal multiple of C, we can convert that multiple into a percent by multiplying by 100. This systematic substitution is the key idea behind the solution. Step-by-Step Solution: Step 1: Write A in terms of B: A = 20% of B = 20 / 100 * B = 0.20 * B.Step 2: Write B in terms of C: B = 25% of C = 25 / 100 * C = 0.25 * C.Step 3: Substitute the expression for B into the equation for A: A = 0.20 * (0.25 * C).Step 4: Multiply the decimals: 0.20 * 0.25 = 0.05.Step 5: So A = 0.05 * C, which means A is 5% of C. Verification / Alternative check: We can verify using assumed numerical values. Let C = 100 units. Then B = 25% of 100 = 25 units. Next, A = 20% of 25 = 5 units. If C is 100 units and A is 5 units, then A is 5 / 100 * 100% = 5% of C. This numerical check confirms the algebraic reasoning and gives the same answer. Why Other Options Are Wrong: 10% would mean A = 0.10 * C, which is double the correct value and would require A to be 40% of B or B to be 50% of C, which is not given. 15% and 20% do not come from multiplying 20% and 25% correctly, and they ignore the fact that two successive reductions are involved. 8% is another distractor that cannot be derived from the given relationships. Common Pitfalls: A frequent error is to add or average the two percentages instead of multiplying them as factors. Another mistake is to mix up which quantity is a percentage of which, for example treating C as a percentage of B instead of the other way around. To avoid confusion, always write down the relationships clearly in equation form and use substitution carefully. Converting all percentages to decimals or simple fractions before multiplying also helps reduce calculation mistakes. Final Answer: Quantity A is 5% of quantity C.

Question 16

At a 10% discount on its marked price, a toaster is sold for Rs. 18,000. What will be its selling price if instead a discount of 37.5% is offered on the same marked price?

Accepted Answer

Introduction / Context: This question combines discount calculation and reverse use of percentage to find the marked price, followed by a second discount scenario. It is typical of profit and loss or pricing problems where the same product is sold under different discount schemes. Understanding how to recover the marked price from a discounted price is a common requirement. Given Data / Assumptions: Selling price of the toaster at 10% discount = Rs. 18,000. That means a discount of 10% was applied on the marked price. We need to find the selling price if a discount of 37.5% is applied instead on the same marked price. No other costs, such as tax or shipping, are included. Concept / Approach: First, express the relationship between marked price and selling price under the 10% discount. If the discount is 10%, the customer pays 90% of the marked price. Thus, selling price = 0.9 * marked price. From this we can find the marked price. Then under the second scenario, we apply the 37.5% discount, so the customer pays 62.5% of the same marked price. Finally, we compute that new selling price and compare it with the options. Step-by-Step Solution: Step 1: Let the marked price be M rupees.Step 2: At a 10% discount, the selling price is 90% of M, so 0.9 * M = 18,000.Step 3: Solve for M: M = 18,000 / 0.9 = 20,000 rupees.Step 4: Under the 37.5% discount, the percentage paid is 100% - 37.5% = 62.5% = 0.625.Step 5: New selling price = 0.625 * M = 0.625 * 20,000 = 12,500 rupees. Verification / Alternative check: We can also think about fractions. A 10% discount leaves 9 parts out of 10, so 9/10 of the marked price equals 18,000, which means each tenth is 2,000 and the full marked price is 20,000. For a 37.5% discount, the customer pays 5/8 of the marked price because 37.5% equals 3/8 and 1 - 3/8 = 5/8. Thus, new selling price = 5/8 of 20,000 = (5 * 20,000) / 8 = 100,000 / 8 = 12,500 rupees. Both methods agree, confirming the answer. Why Other Options Are Wrong: Rs. 7,812.50 corresponds to applying a much larger effective discount and does not match a 37.5% discount on Rs. 20,000. Rs. 8,593.75 and Rs. 15,468.75 are arbitrary looking values that do not correspond to simple fractions of the marked price. Rs. 18,000 is the selling price under the 10% discount scenario and not under the 37.5% discount scenario. Common Pitfalls: Candidates sometimes mistakenly apply the second discount directly on Rs. 18,000, which is wrong because both discounts must be compared with respect to the same marked price. Another frequent mistake is mixing up the percentages for what is paid and what is discounted. Always remember that if discount is d%, then the amount paid is (100 - d)%. Using this idea systematically ensures the correct calculation of both the marked price and the new selling price. Final Answer: The selling price of the toaster with a 37.5% discount on the same marked price is Rs. 12,500.

Question 17

In an examination, a student needs to secure 24% of the maximum marks to pass. The student scores 61 marks and fails by 29 marks. What are the maximum marks for this examination?

Accepted Answer

Introduction / Context: This question focuses on passing marks expressed as a percentage of the maximum marks and uses information about how many marks a student falls short by. Such problems are frequent in aptitude exams and help reinforce the relationship between percentages, absolute marks, and required thresholds. Given Data / Assumptions: A student must secure 24% of the maximum marks to pass. The student actually scores 61 marks. The student fails by 29 marks, which means the student scored that many marks fewer than the passing mark. We need to find the maximum marks for the exam. Concept / Approach: The key observation is that failing by 29 marks means the passing mark is 61 + 29. This passing mark represents 24% of the maximum marks. Once we compute the passing mark, we set up an equation passing mark = 24% of total marks and solve for the total. This is a direct reverse percentage problem in the context of examination scores. Step-by-Step Solution: Step 1: Let the maximum marks be M.Step 2: The passing marks are 24% of M, so passing marks = 24 / 100 * M = 0.24 * M.Step 3: The student scores 61 marks and fails by 29 marks, so passing marks = 61 + 29 = 90 marks.Step 4: Set up the equation 0.24 * M = 90.Step 5: Solve for M: M = 90 / 0.24 = 375. Verification / Alternative check: To verify, calculate 24% of 375. We get 375 * 24 / 100 = 375 * 0.24 = 90 marks. If the passing mark is 90 and the student scored 61, then the shortfall is 90 - 61 = 29 marks, exactly as described in the problem. Therefore, the computed maximum marks of 375 are consistent with all details given in the question. Why Other Options Are Wrong: If the maximum marks were 400, then 24% of 400 would be 96, giving a shortfall of 96 - 61 = 35, not 29. If the maximum marks were 425, then 24% of 425 would be 102, leading to a different shortfall. If the maximum marks were 450, then 24% of 450 would be 108, which does not match the required failing margin. 300 marks would give a passing mark of 72, and the student would fail by only 11 marks, which is again inconsistent. Common Pitfalls: Students sometimes misinterpret "fails by 29 marks" and treat 29 as 24% of the maximum marks, which is incorrect. Another common mistake is to forget to add the shortfall to the obtained marks to compute the passing marks. Always convert verbal descriptions about failure or success into clear equations linking obtained marks, passing marks, and percentages. Writing these relationships step by step avoids confusion and leads to accurate results. Final Answer: The maximum marks for the examination are 375 marks.

Question 18

When a certain number is increased by 24, it becomes 110% of its original value. What is the original number?

Accepted Answer

Introduction / Context: This question checks your understanding of percentage increase and how to convert a statement about increased value into an equation involving the original number. It is a typical reverse percentage problem that can be solved quickly using simple algebra, which is useful in many aptitude tests. Given Data / Assumptions: The original number increases by 24 units. After increasing by 24, the new value is 110% of the original number. We need to find the original number before the increase. Concept / Approach: If the original number is N, then a 10% increase corresponds to multiplying N by 1.10. The statement "becomes 110% of itself" means that the final value is 1.10 * N. Since the final value is also equal to N + 24, we can equate N + 24 with 1.10 * N and solve for N. This is a straightforward linear equation in one variable. Step-by-Step Solution: Step 1: Let the original number be N.Step 2: The new value after increase is N + 24.Step 3: The question says this new value is 110% of the original, so N + 24 = 1.10 * N.Step 4: Rewrite the equation as N + 24 = 1.10 N.Step 5: Subtract N from both sides to get 24 = 0.10 N.Step 6: Solve for N: N = 24 / 0.10 = 240. Verification / Alternative check: Check the result by direct substitution. If the original number is 240, a 10% increase is 240 * 10 / 100 = 24, so the new number becomes 240 + 24 = 264. Now compute 110% of 240: 240 * 110 / 100 = 240 * 1.10 = 264. Since both calculations lead to 264, the result N = 240 is verified. Why Other Options Are Wrong: If N = 288, then 110% of 288 would be 316.8, which is not 288 + 24. If N = 360, 110% of 360 is 396, while 360 + 24 = 384. If N = 216, 110% of 216 is 237.6, not 240. The smaller value 120 gives 110% = 132, whereas 120 + 24 = 144, again not equal. Common Pitfalls: Common errors include interpreting 110% as 10% or adding 24 as if it were 10% of the new value instead of the original. Another mistake is to treat 24 as 10% of the final value instead of the original, which leads to a wrong equation. To avoid confusion, always define the original number as a variable, translate the language about percentages into a clear algebraic equation, and then solve systematically. Final Answer: The original number is 240.

Question 19

Tickets for an adult cost Rs. 2200 and tickets for a child cost Rs. 990. One child can travel free with every two paying adults. If a group consists of 23 adults and 11 children, what is the overall discount percentage that the group receives compar…

Accepted Answer

Introduction / Context: This problem tests percentage discount concepts in the context of a group ticket offer. Instead of a standard percentage discount on price, the offer is framed as free tickets for children under certain conditions. To find the effective discount, we must compare what the group would have paid without the offer to what they actually pay with the offer. This is a realistic commercial arithmetic scenario. Given Data / Assumptions: Adult ticket price = Rs. 2200 each. Child ticket price = Rs. 990 each. Offer: One child goes free for every two paying adults. Group composition: 23 adults and 11 children. The offer is applied as many times as possible using the ratio of 2 adults to 1 free child. Concept / Approach: First, we calculate the total amount the group would pay without any offer. Next, we apply the offer: for every pair of two adults, one child ticket becomes free, up to the number of children available. Then we compute the total amount actually paid under the offer. The effective discount percentage is then (no offer cost - offer cost) / no offer cost * 100. The important part is to match each free child only with complete pairs of adults. Step-by-Step Solution: Step 1: Total cost with no offer: adults cost = 23 * 2200, children cost = 11 * 990.Step 2: Compute adult cost: 23 * 2200 = 50,600 rupees.Step 3: Compute child cost: 11 * 990 = 10,890 rupees.Step 4: Total cost without offer = 50,600 + 10,890 = 61,490 rupees.Step 5: Apply the offer: one free child per two paying adults. With 23 adults, there are 11 full pairs of adults and 1 adult left over.Step 6: The group has 11 children, so all 11 children can go free, because there are 11 pairs of adults.Step 7: Under the offer, the group pays for 23 adult tickets and 0 child tickets.Step 8: Total cost with offer = 23 * 2200 = 50,600 rupees.Step 9: Discount amount = 61,490 - 50,600 = 10,890 rupees.Step 10: Effective discount percentage = (10,890 / 61,490) * 100 ≈ 17.71 percent. Verification / Alternative check: Notice that the discount amount equals the total cost of all 11 children when there is no offer. This is because each child is free under the scheme. So the discount amount should be 11 * 990 = 10,890 rupees, which matches the difference we computed. Dividing this discount by the no offer cost 61,490 gives the effective discount proportion, which evaluates to approximately 0.1771, or 17.71 percent. This confirms the calculation. Why Other Options Are Wrong: 32.30 percent and 26.47 percent would both require a much larger discount amount than the total cost of all children, which is impossible under this scheme. 25.77 percent is close sounding but still significantly larger than the correct discount fraction and does not match the exact calculation. 10 percent represents a much smaller saving than the free travel of 11 children and is therefore clearly incorrect. Common Pitfalls: One common error is to assume that the offer gives a flat percentage discount on all tickets, instead of carefully counting how many children actually get free travel. Another mistake is incorrectly grouping adults and children, for example, assigning more than one free child per pair of adults or forgetting to cap the free children by the actual number of children in the group. Always compute the full price first, then accurately model the offer, and finally compare the two totals to get the effective discount percentage. Final Answer: The group receives an effective discount of approximately 17.71 percent.

Question 20

The marked price of an item is Rs. 500. If a customer buys 2 items, a discount of 8% is given on the total marked price. If a customer buys 3 items, a discount of 16% is given on the total marked price. Radha buys 5 items in one purchase. What is th…

Accepted Answer

Introduction / Context: This question tests the understanding of tiered discount structures. Instead of a single discount rate for any quantity, different discounts apply depending on whether the customer buys 2 items or 3 items. When a customer buys 5 items, we need to decide how to split the purchase across the available discount slabs to compute the total effective discount. Given Data / Assumptions: Marked price of each item = Rs. 500. For buying 2 items together, the discount is 8% on the combined marked price. For buying 3 items together, the discount is 16% on the combined marked price. Radha buys a total of 5 items in one purchase. We assume the best possible use of slabs: 2 items get 8% discount and 3 items get 16% discount. Concept / Approach: We first compute the total amount Radha would pay with no discount. Then we calculate the discounted cost for the group of 2 items and the group of 3 items separately, using their respective discount rates. Adding these gives the actual amount paid. Finally, the effective discount percentage is obtained by comparing the total marked price with this actual payment, using the formula effective discount = (marked total - paid total) / marked total * 100. Step-by-Step Solution: Step 1: Total marked price with no discount = 5 items * Rs. 500 each = Rs. 2,500.Step 2: For the 2 item slab, combined marked price = 2 * 500 = Rs. 1,000.Step 3: Discount on 2 items = 8% of 1,000 = 1,000 * 8 / 100 = Rs. 80, so Radha pays 1,000 - 80 = Rs. 920 for these 2 items.Step 4: For the 3 item slab, combined marked price = 3 * 500 = Rs. 1,500.Step 5: Discount on 3 items = 16% of 1,500 = 1,500 * 16 / 100 = Rs. 240, so Radha pays 1,500 - 240 = Rs. 1,260 for these 3 items.Step 6: Total amount actually paid = 920 + 1,260 = Rs. 2,180.Step 7: Total discount received = original total 2,500 - actual payment 2,180 = Rs. 320.Step 8: Effective discount percentage = (320 / 2,500) * 100 = 12.8 percent. Verification / Alternative check: We can also compute the average discount per item. Total discount is Rs. 320 on 5 items, so discount per item is 320 / 5 = Rs. 64. As a percentage of 500, that is (64 / 500) * 100 = 12.8 percent. This matches the earlier calculation and confirms that the overall effective discount is 12.8 percent. Why Other Options Are Wrong: 20.4 percent and 23.25 percent would both require a larger discount amount than Rs. 320; they do not match the computed figures for slab wise discounts. 12.8 percent is exactly what we derived, so this is the correct choice. 35 percent would correspond to a huge discount of 875 rupees, which is much more than the sum of the slab wise discounts. 16 percent is simply the discount rate for 3 items, not the combined effective rate across 5 items with mixed slabs. Common Pitfalls: A common mistake is to average the two discount percentages (8% and 16%) or to apply 16% on all 5 items, which ignores the slab structure. Another mistake is to forget that discounts apply on the combined marked price for each slab, not on the total original bill directly. To avoid errors, always split the purchase into the defined slabs, compute each part separately, sum the actual payments, and then derive the effective discount from the grand total. Final Answer: Radha receives an overall effective discount of 12.8 percent on her purchase of 5 items.

Percentage Questions