Solved Questions

How to Use These Questions

There are 34 questions here, in no fixed order. A false-weight question can come right after one on marked price, so first decide which price each percentage is on: the CP, the SP or the MP. After that, most of them take one or two lines.

Cover the answer and work each question on paper with a timer running. Somewhere between 36 and 45 seconds is Tier 1 speed. If one takes you over a minute, look in Shortcuts & Speed Methods for the route that would have saved the time, and redo the question the next day.

About a quarter of the questions are basics: CP, SP and profit %, extra costs added to CP, and CP from two selling prices. Another quarter are articles bought and sold at different rates, two items sold together, parts of a stock at different rates and changing prices. About 30% are marked price and discount of every kind (markup with discount, the MP needed for a target profit, successive discounts, buy x get y free, trade and cash discounts, GST on a discounted price). The rest are false weights, chains of sales, commission and wastage.

Questions marked [Tier 2] need a less obvious setup, such as eggs bought at two rates and sold at a third, or a trader cheating while buying and while selling. If Tier 1 is your only paper, still try them: shorter versions of the same setups turn up there.

Solved Examples

Question 1

A man buys a second-hand fridge for ₹6,250. He spends ₹350 on transport and ₹400 on repairs. At what price must he sell it to gain 12%?

Answer. Transport and repairs are part of the cost, so CP = 6,250 + 350 + 400 = ₹7,000. SP = 7,000 × 1.12 = ₹7,840. If you put the 12% on ₹6,250 alone and add the extras afterwards, you get ₹7,750, which is short.

Question 2

A shopkeeper marks an article 32% above its cost price and then allows a 25% discount. Does he gain or lose, and by what %?

Answer. I multiply the two factors: 1.32 × 0.75 = 0.99. So he loses 1%. Doing 32 − 25 = 7% gain is the usual mistake. The discount is taken on the bigger marked price, so it eats up more than 25% of the cost.

Question 3

A shopkeeper buys pens at 20 for ₹150 and sells them at 16 for ₹136. Find his profit %.

Answer. The LCM of 20 and 16 is 80. 80 pens cost 4 × 150 = ₹600 and sell for 5 × 136 = ₹680. Profit = 80 on 600 = $13\frac{1}{3}\%$. Per pen it's the same thing: he buys at ₹7.50 and sells at ₹8.50.

Question 4

A shopkeeper sells his goods at a 12% profit, but his weight is 4% less than it should be. Find his actual gain %.

Answer. For every kg he charges for, he gives only 0.96 kg. So his gain factor is $\frac{1.12}{0.96} = \frac{7}{6}$, which is a $16\frac{2}{3}\%$ gain. Adding 12 + 4 = 16% is wrong, because the short weight works on a smaller base.

Question 5

The difference between the selling prices of an article at a 16% gain and at a 4% loss is ₹550. Find its cost price.

Answer. One gain and one loss, so the gap is 16 + 4 = 20% of the CP. 20% is ₹550, so CP = ₹2,750. Check: 3,190 − 2,640 = 550.

Question 6

A trader buys a sofa for ₹9,600. He wants a 15% profit even after giving a 20% discount. What price should he mark on it?

Answer. MP = 9,600 × $\frac{115}{80}$ = ₹13,800. Check: 20% off ₹13,800 is ₹11,040, and 9,600 × 1.15 is also ₹11,040.

Question 7

Two scooters are sold for ₹39,100 each, one at a 15% gain and the other at a 15% loss. Find the total gain or loss.

Answer. Same SP and the same %, so overall it's a loss of $\frac{15^2}{100}$ = 2.25%. For the rupees I find the CPs: 39,100 ÷ 1.15 = ₹34,000 and 39,100 ÷ 0.85 = ₹46,000. Total CP is ₹80,000 and total SP is ₹78,200, so it's a loss of ₹1,800. That is 2.25% of ₹80,000, as it should be.

Question 8

A manufacturer sells a cooler to a wholesaler at a 20% profit. The wholesaler sells it to a retailer at a 15% profit, and the retailer sells it to a customer at a 25% profit. The customer pays ₹4,830. What did it cost the manufacturer?

Answer. The three profits multiply: 1.2 × 1.15 × 1.25 = 1.725. So the manufacturer's cost = 4,830 ÷ 1.725 = ₹2,800. Going forward to check: 2,800 becomes 3,360, then 3,864, then 4,830.

Question 9

A man sold a cycle for ₹3,264 at a loss of 15%. At what price should he have sold it to gain 10%?

Answer. ₹3,264 is 85% of the CP, so CP = 3,264 ÷ 0.85 = ₹3,840. For a 10% gain, SP = 3,840 × 1.1 = ₹4,224. In one step: 3,264 × $\frac{110}{85}$ = 4,224.

Question 10

The ratio of the marked price to the cost price of an article is 9 : 5. If a 15% discount is given, find the profit %.

Answer. I take MP = 9 and CP = 5. After 15% off, SP = 9 × 0.85 = 7.65. The profit is 2.65 on 5, which is 53%.

Question 11

A man sells an article at a 15% gain. Had he bought it at 10% less and sold it for ₹165 more, he would have gained 40%. Find the cost price.

Answer. CP = 100 units and SP = 115. In the "what if" case, CP = 90 and SP = 90 × 1.4 = 126. The new SP is 11 units more, and that is ₹165, so one unit is ₹15 and CP = ₹1,500. Check: SP = ₹1,725, and in the other case CP = ₹1,350 and SP = ₹1,890, which is 1,725 + 165.

Question 12

Three shops sell the same TV at the same marked price. Shop A gives 33% off. Shop B gives two successive discounts of 18% each. Shop C gives successive discounts of 15%, 12% and 10%. Which shop sells it cheapest?

Answer. A gives 33%. B gives 18 + 18 − 3.24 = 32.76%. At C you pay 0.85 × 0.88 × 0.9 = 0.6732 of the price, so the discount is 32.68%. The biggest discount is at shop A, so it's the cheapest. B and C add up to 36% and 37%, which makes them look better, but successive discounts always come to less than their sum.

Question 13

A trader's profit is 28% of his selling price. What is his profit % on the cost price?

Answer. I take SP = 100. Profit = 28, so CP = 72. Profit on cost = $\frac{28}{72} = \frac{7}{18}$, which is $38\frac{8}{9}\%$.

Question 14

A vendor sells 36 oranges for ₹162 and loses 10%. How many oranges must he sell for ₹162 to gain 20%?

Answer. ₹162 is 90% of the cost of 36 oranges, so they cost ₹180, which is ₹5 each. For a 20% gain each orange must fetch ₹6, so ₹162 should buy 27 oranges. Quick way: 36 × $\frac{90}{120}$ = 27.

Question 15

A farmer sells his crop through an agent who keeps 6% of the sale price as commission. The crop cost the farmer ₹24,000, and he wants a 17.5% profit after paying the agent. At what price must the agent sell it?

Answer. The farmer needs 24,000 × 1.175 = ₹28,200 in hand, and he keeps 94% of the sale price. So the sale price = 28,200 ÷ 0.94 = ₹30,000. Check: 6% of ₹30,000 is ₹1,800, and 30,000 − 1,800 = 28,200.

Question 16

After successive discounts of 24% and 5%, a jacket sells for ₹2,527. What is its marked price?

Answer. The buyer pays 0.76 × 0.95 = 0.722 of the MP. So MP = 2,527 ÷ 0.722 = ₹3,500. Adding the discounts to 29% and dividing by 0.71 gives about ₹3,559, which is wrong.

Question 17 [Tier 2]

A man buys the same number of eggs at 3 for ₹10 and at 5 for ₹10, mixes them, and sells all of them at 4 for ₹10. Find his gain or loss %.

Answer. I take 15 eggs of each kind (the LCM of 3 and 5). They cost ₹50 and ₹30, so 30 eggs cost ₹80. Selling 30 eggs at 4 for ₹10 brings in ₹75. So he loses ₹5 on ₹80, which is 6.25%. "4 for ₹10" looks like the middle rate, but his average cost is about ₹2.67 an egg, more than the ₹2.50 he sells at.

Question 18

A shopkeeper sells a lamp at a 6% loss. Had he sold it for ₹198 more, he would have made a 5% gain. At what price should he sell it to gain 20%?

Answer. The ₹198 covers 6% + 5% = 11% of the CP, so 1% is ₹18 and CP = ₹1,800. For a 20% gain, SP = 1,800 × 1.2 = ₹2,160.

Question 19

An article that costs ₹1,200 is marked at ₹1,650. It is sold at a 21% profit. What % discount was given?

Answer. SP = 1,200 × 1.21 = ₹1,452. The discount is 1,650 − 1,452 = ₹198, and on the marked price that is $\frac{198}{1650}$ = 12%. Working it out on the cost price gives 16.5%, which is the usual slip.

Question 20

A vendor buys 360 bananas at ₹5 each, and $\frac{1}{9}$ of them rot. At what price must he sell each of the rest to make a 28% profit on the whole?

Answer. The total cost is ₹1,800, so he needs 1,800 × 1.28 = ₹2,304. Only 320 bananas are left, so each must sell for 2,304 ÷ 320 = ₹7.20. In one line: 5 × 1.28 × $\frac{9}{8}$ = 7.2.

Question 21

Two watches cost ₹8,100 together. One is sold at a 15% gain and the other at an 8% loss, and both fetch the same price. Find the cost of each watch and the overall gain or loss.

Answer. Same SP, so 1.15 × (first CP) = 0.92 × (second CP). That makes first CP : second CP = 0.92 : 1.15 = 4 : 5, so the costs are ₹3,600 and ₹4,500. Each sells for ₹4,140, so ₹8,280 comes in against ₹8,100, a gain of ₹180, which is $2\frac{2}{9}\%$.

Question 22

A shopkeeper marks his goods 20% above cost and runs a "buy 5, get 1 free" offer. Find his profit or loss %.

Answer. A customer takes 6 and pays for 5, so each article sells at $\frac{5}{6}$ of its MP. The factor is 1.2 × $\frac{5}{6}$ = 1, so he makes no profit and no loss. The 20% markup looks like a profit, but the free article takes all of it back.

Question 23 [Tier 2]

An article is sold for ₹171, and the gain % is the same number as the cost price in rupees. Find the cost price.

Answer. If the CP is ₹c, the gain is c% of c, which is $\frac{c^2}{100}$. So c + $\frac{c^2}{100}$ = 171. Trying c = 90 gives 90 + 81 = 171, so the CP is ₹90. (In full, $c^2 + 100c - 17100 = 0$, and the other root is negative.)

Question 24

A wholesaler's list price for a sewing machine is ₹22,000. He gives a retailer an 18% trade discount and a further 2.5% cash discount for paying in cash. How much does the retailer pay?

Answer. After the trade discount: 22,000 × 0.82 = ₹18,040. After the cash discount: 18,040 × 0.975 = ₹17,589. The cash discount is on ₹18,040, not on the list price, so taking 20.5% off in one go (₹17,490) is wrong.

Question 25

A shop sells 500 bags a month at ₹320 each, and each bag costs it ₹240. It raises the price by 15%, and its monthly sales fall by 25%. By how much does its monthly profit change?

Answer. Before: 500 × 80 = ₹40,000. After: the price is ₹368, so the profit on a bag is ₹128, and 375 bags are sold, which gives ₹48,000. So the monthly profit goes up by ₹8,000, even though a quarter of the sales are lost. The cost of a bag stays at ₹240, so a 15% price rise lifts the profit on each bag by 60%.

Question 26

A trader marks his goods 25% above cost, gives a 4% discount, and uses an 800 g weight in place of 1 kg. Find his gain %.

Answer. I multiply all three factors: 1.25 × 0.96 × $\frac{1000}{800}$ = 1.2 × 1.25 = 1.5. So he gains 50%.

Question 27

The gain on selling a book for ₹486 is twice the gain on selling it for ₹438. Find its cost price.

Answer. If the CP is C, then 486 − C = 2(438 − C), so C = 2 × 438 − 486 = ₹390. Check: the gains are ₹96 and ₹48.

Question 28

A pressure cooker is marked at ₹3,200. The shop gives a 12.5% discount, and then 12% GST is charged on the discounted price. How much does the customer pay?

Answer. After the discount the price is 3,200 × $\frac{7}{8}$ = ₹2,800. GST goes on top of this: 2,800 × 1.12 = ₹3,136.

Question 29

A trader sells $\frac{1}{4}$ of his stock at a 20% profit and $\frac{1}{3}$ of it at a 12% profit. He gains 9% on the whole. What does he make on the rest?

Answer. The rest is 1 − $\frac{1}{4}$ − $\frac{1}{3}$ = $\frac{5}{12}$ of the stock. Weighting each rate by its share: $\frac{1}{4}$ × 20 + $\frac{1}{3}$ × 12 + $\frac{5}{12}$ × r = 9, which is 5 + 4 + $\frac{5r}{12}$ = 9. So r = 0, and the rest is sold at no profit and no loss.

Question 30 [Tier 2]

A trader marks an article at ₹1,850. The discount he gives (in rupees) equals the profit he makes, and his profit is 12.5%. What % discount does he give?

Answer. Discount = profit means the SP is exactly halfway between the CP and the MP. With CP = 8 units, a 12.5% profit makes SP = 9 units, so MP = 10 units. 10 units = ₹1,850, so one unit is ₹185. The discount is 1 unit out of 10, which is 10%. (CP = ₹1,480 and SP = ₹1,665, so both the discount and the profit are ₹185.)

Question 31

A tailor buys cloth for ₹12,600 and makes 35 shirts from it. He pays ₹120 a shirt for stitching and ₹20 a shirt for packing, and sells each shirt for ₹620. Find his profit %.

Answer. Cost of one shirt = 12,600 ÷ 35 + 120 + 20 = 360 + 140 = ₹500. The profit is ₹120 on ₹500, which is 24%. Leaving out the stitching and packing would give about 72%, which is far too high.

Question 32

In making a toy, material is $\frac{3}{5}$ of the cost and labour is the rest. The toy was sold at a 33% profit. Then the price of material goes up by 20% and labour by 5%, but the selling price stays the same. What is the profit % now?

Answer. I take the cost as 100: material 60 and labour 40. After the rise, material is 72 and labour is 42, so the cost is 114. The SP stays at 133, so the profit is 19 on 114 = $\frac{1}{6}$, which is $16\frac{2}{3}\%$.

Question 33

X sold a scooter to Y at an 8% profit, and Y sold it to Z at a 5% loss. Z paid ₹55,404. How much did X pay for it?

Answer. The chain multiplies to 1.08 × 0.95 = 1.026. So X paid 55,404 ÷ 1.026 = ₹54,000. Going forward to check: 54,000 becomes 58,320, then 55,404.

Question 34 [Tier 2]

A dishonest trader takes 12% more than he pays for when he buys, and gives 12% less than he charges for when he sells. He buys and sells at the same price per kg. Find his gain %.

Answer. For every kg he pays for, he gets 1.12 kg. Every 0.88 kg he hands over is charged as a full kg. So his gain factor is $\frac{1.12}{0.88} = \frac{14}{11}$, a gain of $27\frac{3}{11}\%$. Adding 12 + 12 = 24% is too low, because the second 12% works on a smaller base.