Profit and Loss Basics

Cost Price, Selling Price, Profit and Loss

Every profit and loss question is about two prices.

• Cost price (CP): what the seller paid for the article. If he also paid for repairs, transport or making it, that goes into the CP too (more on this near the end of this section).
• Selling price (SP): what the buyer pays him.

If the SP is more than the CP, the difference is a profit (or gain). If the SP is less than the CP, the difference is a loss. If the two are equal, it is "no profit, no loss".

$$\text{Profit} = \text{SP} - \text{CP} \qquad \text{Loss} = \text{CP} - \text{SP}$$

Profit % and loss % are always on the CP, unless the question clearly says "on the selling price".

$$\text{Profit}\% = \frac{\text{Profit}}{\text{CP}} \times 100 \qquad \text{Loss}\% = \frac{\text{Loss}}{\text{CP}} \times 100$$

A profit. A bag bought for ₹640 is sold for ₹752. Profit = ₹112, and profit % = $\frac{112}{640} \times 100$ = 17.5%.

A loss. A phone bought for ₹8,400 is sold for ₹7,686. Loss = ₹714, and loss % = $\frac{714}{8400} \times 100$ = 8.5%.

From a ratio. When CP : SP is given, treat the two terms as rupees. CP : SP = 15 : 17 means a profit of 2 on 15, which is $\frac{2}{15}$ = $13\frac{1}{3}\%$. SP : CP = 7 : 8 means a loss of 1 on 8, which is 12.5%. Watch the order, because SSC writes it both ways.

From "CP is x% of SP". If the CP is 80% of the SP, then CP : SP = 80 : 100 = 4 : 5, and the profit is 1 on 4, which is 25%, not 20%.

Fractions to know as percentages. Profit questions turn into fractions all the time, so it helps to know the fraction and percent table (see Chapter 3) by heart.

Marked price and discount have their own section (Marked Price and Discount), and so do false weights and chains of sales (Dishonest Dealers and Successive Transactions). This section sticks to plain buying and selling.

[SSC Tip] In the bag question, ₹112 on the SP of ₹752 is about 14.9%. SSC puts that number in the options for anyone who divides by the wrong price. Before you divide, say to yourself "on the cost".

The Multiplier: From CP to SP and Back

Instead of finding the profit and adding it on, multiply the CP by one number.

$$\text{SP} = \text{CP} \times \frac{100 + \text{profit}\%}{100} \qquad \text{SP} = \text{CP} \times \frac{100 - \text{loss}\%}{100}$$

Forward. A cooler costs ₹1,850 and is sold at a 12% profit: SP = 1,850 × 1.12 = ₹2,072. A sofa costing ₹3,200 is sold at a 15% loss: SP = 3,200 × 0.85 = ₹2,720.

Backward. To get the CP from the SP, divide by the same multiplier.

$$\text{CP} = \text{SP} \times \frac{100}{100 + \text{profit}\%} \qquad \text{CP} = \text{SP} \times \frac{100}{100 - \text{loss}\%}$$

• Sold for ₹1,365 at a 5% profit: CP = 1,365 × $\frac{100}{105}$ = ₹1,300.
• Sold for ₹3,519 at an 8% loss: CP = 3,519 × $\frac{100}{92}$ = ₹3,825.

The big trap. Going backwards, never take the percentage off the SP. A kettle sold for ₹1,476 at a 20% profit cost 1,476 ÷ 1.2 = ₹1,230. Taking 20% off ₹1,476 gives ₹1,180.80, which is wrong, because the 20% was worked out on ₹1,230 and not on ₹1,476. Check: 1,230 + 246 = 1,476.

Fraction multipliers are faster.

So an article sold for ₹2,856 at a $16\frac{2}{3}\%$ profit cost 2,856 × $\frac{6}{7}$ = ₹2,448. Practise seeing 1.12, 0.85, $\frac{6}{5}$ and $\frac{7}{8}$ as single steps: later questions chain two or three of them, and that stays quick only if each step is one multiplication.

Profit in rupees and profit %. Profit = CP × $\frac{p}{100}$, so CP = profit × $\frac{100}{p}$. A trader who makes ₹378 at a 14% profit had a CP of 378 × $\frac{100}{14}$ = ₹2,700.

Sum of CP and SP. "The CP and SP of a clock add up to ₹4,305 and the profit is 5%." CP : SP = 100 : 105 = 20 : 21, so the 41 parts are ₹4,305 and one part is ₹105. CP = 20 × 105 = ₹2,100 and SP = ₹2,205.

Selling Price for a Target, and Moving from One Price to Another

SP for a target profit or loss. Multiply the CP by the multiplier for the target. A dealer pays ₹4,600 for a TV stand and wants a 15% profit: SP = 4,600 × 1.15 = ₹5,290. To clear an old item that cost ₹3,250 at no more than a 6% loss, the lowest price is 3,250 × 0.94 = ₹3,055.

After a first sale made a loss. "By selling a watch for ₹1,710 a man loses 10%. At what price should he sell it to gain 12%?"

• CP = 1,710 ÷ 0.9 = ₹1,900.
• SP for a 12% gain = 1,900 × 1.12 = ₹2,128.

You don't need the CP at all. The old SP is 90% of the CP and the new SP is 112% of it, so

$$\text{new SP} = \text{old SP} \times \frac{100 \pm \text{new}\%}{100 \pm \text{old}\%} = 1710 \times \frac{112}{90} = 2128$$

The same rule moves from one gain to another. Sold for ₹2,322 at an 8% gain; for a 20% gain, sell at 2,322 × $\frac{120}{108}$ = ₹2,580.

New profit % from a new price. "Sold for ₹1,710 at a 10% loss. What is the gain % if it is sold for ₹2,014?" The CP is ₹1,900, so the gain is 2,014 − 1,900 = ₹114, which is $\frac{114}{1900}$ = 6%. Always go back to the CP. A percentage worked out on one SP can't be added to a percentage worked out on another.

The adding trap. In the watch question, some students add 10% + 12% = 22% to ₹1,710 and get ₹2,086.20. Both the 10% and the 12% are on the CP, not on ₹1,710, so this is wrong.

[Tier 2] Profit % equal to the cost price. "An article is sold for ₹96, and the profit % equals its CP in rupees." If CP = x, the profit is x% of x, which is $\frac{x^2}{100}$, so

$$x + \frac{x^2}{100} = 96 \Rightarrow x^2 + 100x - 9600 = 0 \Rightarrow (x - 60)(x + 160) = 0$$

So the CP is ₹60, and the profit is 60% of 60 = ₹36. In the exam, test the options instead: 60 + 36 = 96 fits at once.

Profit on the Selling Price, and Profit as a Fraction

Some questions give the profit as a share of the SP. Turn it into a share of the CP before you answer, because "profit %" with nothing after it means on the CP.

Profit as a % of the SP. "A trader's profit is 25% of his selling price." Take SP = 100. Profit = 25, so CP = 75, and the profit on the CP is $\frac{25}{75}$ = $33\frac{1}{3}\%$. In general, if p and l are the profit and the loss as a % of the SP,

$$\text{profit on CP} = \frac{p}{100 - p} \times 100 \qquad \text{loss on CP} = \frac{l}{100 + l} \times 100$$

A loss of 20% of the SP: SP = 100 and CP = 120, so the loss on the CP is $\frac{20}{120}$ = $16\frac{2}{3}\%$.

Going the other way, a profit of p% on the CP is $\frac{p}{100 + p} \times 100$ percent of the SP. A 25% profit on the CP is 20% of the SP.

Profit or loss as a fraction. There are four cases (n is a whole number):

Same SP, two readings. A chair is sold for ₹2,730.

• If the gain is $\frac{1}{6}$ of the CP, CP : SP = 6 : 7, so CP = 2,730 × $\frac{6}{7}$ = ₹2,340.
• If the gain is $\frac{1}{6}$ of the SP, the gain is ₹455 and the CP is ₹2,275, so the gain is $\frac{455}{2275}$ = 20%.

The two readings give different answers, and both are usually offered as choices, so underline the word after "of" before you start.

A loss as a fraction of the SP. "The loss is $\frac{1}{9}$ of the selling price." CP : SP = 10 : 9, so the loss % is $\frac{1}{10}$ = 10%, not $11\frac{1}{9}\%$.

CP from Two Selling Prices: Equal Gain and Loss

A common CGL question gives two selling prices of the same article, one above the CP and one below it, and ties the gain at one to the loss at the other.

Gain at one price = loss at the other. "The profit on selling a cycle for ₹6,380 equals the loss on selling it for ₹5,140." The CP sits exactly halfway between the two prices:

$$\text{CP} = \frac{\text{SP}_1 + \text{SP}_2}{2} = \frac{6380 + 5140}{2} = 5760$$

Check: 6,380 − 5,760 = ₹620 and 5,760 − 5,140 = ₹620. A follow-up often asks for the SP that gives a 25% profit: 5,760 × 1.25 = ₹7,200.

Gain % at one price = loss % at the other. Both percentages are on the same CP, so equal percentages mean equal rupees, and the same average works.

Gain = k times the loss. Now the CP is not the midpoint; it sits closer to the price that gives the loss. With $\text{SP}_1$ giving the profit and $\text{SP}_2$ the loss,

$$\text{CP} = \frac{\text{SP}_1 + k \times \text{SP}_2}{k + 1}$$

"The profit when a heater is sold for ₹1,340 is three times the loss when it is sold for ₹980." CP = $\frac{1340 + 3 \times 980}{4} = \frac{4280}{4}$ = ₹1,070. Check: profit = ₹270, loss = ₹90, and 270 = 3 × 90. Why it works: if CP = c, then 1,340 − c = 3(c − 980), so 4c = 1,340 + 2,940.

[Tier 2] Gain is some % more than the loss. "The profit on selling at ₹760 is 20% more than the loss on selling at ₹650." Here k = 1.2, so CP = $\frac{760 + 1.2 \times 650}{2.2} = \frac{1540}{2.2}$ = ₹700. Check: profit ₹60, loss ₹50, and 60 is 20% more than 50.

Gain more than the loss by some rupees. "The profit at ₹980 is ₹40 more than the loss at ₹800." With CP = c, (980 − c) − (c − 800) = 40, so 2c = 1,740 and c = ₹870. Check: profit ₹110, loss ₹70.

[SSC Tip] Put the multiplier k on the price that gives the loss. Putting it on the wrong price gives (3 × 1,340 + 980) ÷ 4 = ₹1,250 in the heater question, which SSC will happily offer. If the profit is k times the loss, the CP must lie nearer the lower price.

CP from Two Selling Prices: The Difference Method

When the question gives the difference between two selling prices and the two percentages, the CP comes from one division. Both SPs are percentages of the same CP, so

$$\text{difference of the SPs} = \text{difference of the percentages} \times \text{CP}$$

Count a profit as plus and a loss as minus.

Two profits. "A cooler is sold at a 14% profit. Had it been sold at a 9% profit, the seller would have got ₹235 less." The gap is 14 − 9 = 5% of the CP, so CP = 235 × $\frac{100}{5}$ = ₹4,700.

A loss, then a profit. "A man sold a sofa at a 7% loss. If he had sold it for ₹1,224 more, he would have gained 11%." From −7% to +11% is a jump of 18%, so CP = 1,224 × $\frac{100}{18}$ = ₹6,800. He actually sold it for 6,800 × 0.93 = ₹6,324.

A profit, then a loss. "A dealer gains 6% on a fan. Had he sold it for ₹168 less, he would have lost 8%." The gap is 6 + 8 = 14%, so CP = 168 × $\frac{100}{14}$ = ₹1,200.

Two losses. "Sold at an 18% loss. For ₹390 more, the loss would have been only 12%." The gap is 6%, so CP = 390 × $\frac{100}{6}$ = ₹6,500.

The difference stated directly. "The SP at a 12% gain and the SP at an 8% loss differ by ₹500." Again 20% of the CP = ₹500, so CP = ₹2,500.

The trap. In the sofa question, 11 − 7 = 4% gives CP = 1,224 ÷ 0.04 = ₹30,600. Going from a 7% loss to an 11% gain, the price first climbs 7% back up to the CP and then another 11%, so the gap is 18%, not 4%.

[SSC Tip] Draw a quick number line with the CP at 100: an 18% loss sits at 82, a 12% loss at 88 and an 11% gain at 111. The rupee difference is the distance between the two marks. The picture also shows at once which SP is bigger, which helps when the question says "₹x less" instead of "₹x more".

Overheads: Repairs, Transport, Packing and Tax

The cost price is everything the seller spends to get the article ready for sale, not just the price he paid for it. Repairs, transport (freight or cartage), loading, packing, registration and any tax he paid while buying all go into the CP, unless the question says the expense came after the sale. The profit % is then worked out on this total.

$$\text{CP} = \text{purchase price} + \text{overheads}$$

Repairs. Arjun buys a second-hand bike for ₹38,500 and spends ₹4,500 on repairs. He sells it for ₹49,450.

• CP = 38,500 + 4,500 = ₹43,000.
• Profit = 49,450 − 43,000 = ₹6,450, which is $\frac{6450}{43000} \times 100$ = 15%.

The common wrong answer is 10,950 ÷ 38,500, about 28.4%, which forgets the repairs.

Transport on a lot. A vendor buys 150 kg of tomatoes at ₹24 per kg and pays ₹300 to bring them to his shop. Total CP = 3,600 + 300 = ₹3,900, which is ₹26 per kg. For a 20% profit he must sell at 26 × 1.2 = ₹31.20 per kg, not 24 × 1.2 = ₹28.80.

Tax paid while buying. A shopkeeper buys a fridge for ₹18,000 and pays 12% tax on it, so his CP is 18,000 × 1.12 = ₹20,160. Selling it for ₹22,176 gives him ₹2,016, which is 10%. (Tax charged to a customer on a discounted price is in the Marked Price and Discount section.)

Finding the purchase price backwards. "A dealer spent ₹1,200 on repairs to a machine and sold it for ₹15,180 at a 15% profit. What did he pay for it?" Total CP = 15,180 ÷ 1.15 = ₹13,200, so he paid 13,200 − 1,200 = ₹12,000. Find the total CP first and take the overheads off at the end. Taking 15% off ₹15,180, or leaving the repairs inside, gives the wrong options SSC loves.

Making Charges, Profit per Article and Total Profit

Making or labour charges are part of the CP. A carpenter buys wood for ₹2,600, pays ₹1,400 for labour and ₹200 for polish, and sells the table for ₹5,040.

• CP = 2,600 + 1,400 + 200 = ₹4,200.
• Profit = ₹840, which is $\frac{840}{4200} \times 100$ = 20%.

The same goes for a goldsmith's making charges, a tailor's stitching or a bakery's gas bill. If it was spent to make the article, it is in the CP.

Profit per article. When every article costs the same and sells at the same price, work with one article and multiply. A stationer buys 240 pens at ₹12.50 each and sells them at ₹15 each.

• Profit per pen = ₹2.50, which is $\frac{2.5}{12.5}$ = 20%.
• Total profit = 240 × 2.50 = ₹600, and on the total CP of ₹3,000 that is again 20%.

Profit % per article and profit % on the whole lot are the same, as long as all the articles are alike.

How many to sell for a target profit. Divide the target by the profit per article. At ₹2.50 a pen, a profit of ₹1,000 needs 1,000 ÷ 2.5 = 400 pens. Dividing the target by the SP or by the CP gives the usual wrong options.

A fixed cost to cover first. A juice stall pays ₹600 a day as rent. Each glass costs ₹8 to make and sells for ₹12, a profit of ₹4. The first 600 ÷ 4 = 150 glasses only pay the rent. For a net profit of ₹1,000 a day the stall must sell (600 + 1,000) ÷ 4 = 400 glasses.

Profit as a share of the takings. Daily sales of ₹6,300 at a 25% profit on cost mean the cost was 6,300 ÷ 1.25 = ₹5,040, so the profit is ₹1,260, not 25% of ₹6,300 = ₹1,575. The multiplier from earlier in this section works on totals exactly as it does on one article.

Solved Examples

Question 1

A trader buys a mixer grinder for ₹3,250 and sells it for ₹3,705. What is his profit percentage? (a) 12.28% (b) 14% (c) 15% (d) 13%

Answer. Profit = 3,705 − 3,250 = ₹455. Profit % is on the CP, so it is $\frac{455}{3250} \times 100$ = (b) 14%. If you divide by the SP instead, you get 455 ÷ 3,705 = 12.28%, which is the usual trap.

Question 2

The ratio of the cost price to the selling price of a lamp is 25 : 21. What is the loss percentage? (a) 19.05% (b) 4% (c) 16% (d) 21%

Answer. Take CP = ₹25 and SP = ₹21. The loss is ₹4 on a CP of ₹25, so the loss % is $\frac{4}{25} \times 100$ = (c) 16%.

Question 3

By selling a table for ₹4,968, a carpenter gains 15%. What did the table cost him? (a) ₹4,222.80 (b) ₹4,200 (c) ₹5,713.20 (d) ₹4,320

Answer. SP = CP × 1.15, so CP = 4,968 ÷ 1.15 = (d) ₹4,320. Check: 15% of 4,320 is 648, and 4,320 + 648 = 4,968. Taking 15% off ₹4,968 gives ₹4,222.80, but that treats the 15% as if it were on the SP.

Question 4

The cost price and the selling price of a bag add up to ₹2,666, and the profit is 15%. What is the profit? (a) ₹186 (b) ₹199.95 (c) ₹399.90 (d) ₹1,240

Answer. CP : SP = 100 : 115 = 20 : 23. So ₹2,666 is 43 parts, and one part is ₹62. CP = 20 × 62 = ₹1,240 and SP = 23 × 62 = ₹1,426, so the profit is (a) ₹186. Check: 15% of 1,240 is 186.

Question 5

A man sold a cupboard for ₹7,040 at a loss of 12%. At what price should he have sold it to gain 15%? (a) ₹8,096 (b) ₹9,200 (c) ₹8,940.80 (d) ₹8,800

Answer. First the CP: 7,040 ÷ 0.88 = ₹8,000. For a 15% gain, SP = 8,000 × 1.15 = (b) ₹9,200. In one line: 7,040 × $\frac{115}{88}$ = 9,200. Adding 12% + 15% = 27% to ₹7,040 gives ₹8,940.80, which starts from the old SP instead of the CP.

Question 6

A dealer sells a sofa for ₹16,330 at a profit of 15%. If he sells it for ₹13,845 instead, what will be his profit or loss percentage? (a) Loss of 2.5% (b) Loss of 2.95% (c) Gain of 2.5% (d) Loss of 15.22%

Answer. Everything goes back to the CP: 16,330 ÷ 1.15 = ₹14,200. At ₹13,845 he gets ₹355 less than the CP, which is $\frac{355}{14200} \times 100$ = 2.5%. So the answer is (a) Loss of 2.5%.

Question 7

[Tier 2] A man sold an article for ₹119 and gained as much percent as the article cost him in rupees. What was the cost price? (a) ₹85 (b) ₹60 (c) ₹70 (d) ₹90

Answer. Say the CP is ₹x. The profit is x% of x, which is $\frac{x^2}{100}$, so $x + \frac{x^2}{100} = 119$. Testing the options is quicker than solving: for ₹70 the profit is 70% of 70 = ₹49, and 70 + 49 = 119. So the CP is (c) ₹70.

Question 8

A shopkeeper's profit is 37.5% of his selling price. What is his profit percentage on the cost price? (a) 37.5% (b) 60% (c) 27.27% (d) 62.5%

Answer. Take SP = ₹100. The profit is ₹37.50, so the CP is ₹62.50. Profit on the CP = $\frac{37.5}{62.5} \times 100$ = (b) 60%.

Question 9

A man sold a table for ₹1,782, and his loss was $\frac{1}{11}$ of the selling price. What was the cost price? (a) ₹1,620 (b) ₹1,960.20 (c) ₹1,930.50 (d) ₹1,944

Answer. The loss is $\frac{1}{11}$ of 1,782 = ₹162. With a loss, the CP is above the SP, so CP = 1,782 + 162 = (d) ₹1,944. In ratio form, CP : SP = 12 : 11.

Question 10

A shopkeeper sold a heater for ₹3,060, gaining $\frac{1}{8}$ of its cost price. What was the cost price? (a) ₹2,720 (b) ₹2,677.50 (c) ₹2,754 (d) ₹2,550

Answer. A gain of $\frac{1}{8}$ of the CP makes the SP $\frac{9}{8}$ of the CP, so CP : SP = 8 : 9. CP = 3,060 × $\frac{8}{9}$ = (a) ₹2,720. Check: $\frac{1}{8}$ of 2,720 is 340, and 2,720 + 340 = 3,060.

Question 11

The profit earned by selling a watch for ₹2,365 is equal to the loss incurred by selling it for ₹1,795. At what price should it be sold to make a 20% profit? (a) ₹2,838 (b) ₹2,154 (c) ₹2,496 (d) ₹2,580

Answer. Equal profit and loss means the CP is exactly halfway: CP = (2,365 + 1,795) ÷ 2 = ₹2,080. Check: 2,365 − 2,080 = 285 and 2,080 − 1,795 = 285. For a 20% profit, SP = 2,080 × 1.2 = (c) ₹2,496.

Question 12

The profit when a fan is sold for ₹2,175 is twice the loss when it is sold for ₹1,650. What is the cost price of the fan? (a) ₹2,000 (b) ₹1,825 (c) ₹1,912.50 (d) ₹1,800

Answer. Let the CP be c. Then 2,175 − c = 2(c − 1,650), so 3c = 2,175 + 3,300 = 5,475 and c = (b) ₹1,825. Check: profit = ₹350, loss = ₹175, and 350 is twice 175. Putting the 2 on the wrong price gives ₹2,000.

Question 13

A man sold a mobile phone at a loss of 9%. Had he sold it for ₹2,640 more, he would have gained 13%. What is the cost price of the phone? (a) ₹66,000 (b) ₹11,000 (c) ₹14,400 (d) ₹12,000

Answer. From a 9% loss to a 13% gain is a jump of 9 + 13 = 22% of the CP. So 22% of the CP is ₹2,640, and CP = 2,640 × $\frac{100}{22}$ = (d) ₹12,000. Check: 12,000 × 0.91 = 10,920 and 12,000 × 1.13 = 13,560, which differ by 2,640. Using 13 − 9 = 4% would give ₹66,000.

Question 14

A shopkeeper sells a cooler at a 16% profit. If he had sold it at an 11% profit, he would have got ₹540 less. What is the selling price of the cooler? (a) ₹12,528 (b) ₹10,800 (c) ₹11,988 (d) ₹12,960

Answer. The gap is 16 − 11 = 5% of the CP, so CP = 540 × 20 = ₹10,800. The SP at a 16% profit is 10,800 × 1.16 = (a) ₹12,528.

Question 15

A trader sells a printer at a loss of 20%. If he had sold it for ₹1,320 more, his loss would have been only 8%. What is the cost price of the printer? (a) ₹6,600 (b) ₹8,800 (c) ₹11,000 (d) ₹10,120

Answer. Both are losses, so the gap is 20 − 8 = 12% of the CP. CP = 1,320 × $\frac{100}{12}$ = (c) ₹11,000. Check: at a 20% loss he gets ₹8,800 and at an 8% loss ₹10,120, and the difference is ₹1,320. Adding 20 + 8 would be wrong here, because both prices are below the CP.

Question 16

Ravi buys a used car for ₹2,85,000. He spends ₹35,000 on repairs and ₹10,000 on registration, and then sells it for ₹3,63,000. What is his gain percentage? (a) 27.37% (b) 9.09% (c) 10% (d) 12%

Answer. His real CP is 2,85,000 + 35,000 + 10,000 = ₹3,30,000. The gain is 3,63,000 − 3,30,000 = ₹33,000, which is $\frac{33000}{330000} \times 100$ = (c) 10%. Leaving out the repairs and registration gives 27.37% (78,000 ÷ 2,85,000).

Question 17

A dealer spends ₹1,800 on transport and ₹600 on packing a consignment of goods. He sells the consignment for ₹52,920 at a profit of 8%. How much did he pay for the goods? (a) ₹49,000 (b) ₹46,286.40 (c) ₹51,400 (d) ₹46,600

Answer. The total CP is 52,920 ÷ 1.08 = ₹49,000. That includes ₹1,800 + ₹600 = ₹2,400 of overheads, so the goods themselves cost 49,000 − 2,400 = (d) ₹46,600.

Question 18

A tailor buys cloth for ₹1,350, pays ₹450 for stitching and ₹200 for buttons and lining, and sells the suit for ₹2,300. What is his profit percentage? (a) 15% (b) 13.04% (c) 70.37% (d) 17.5%

Answer. Everything he spent to make the suit is in the CP: 1,350 + 450 + 200 = ₹2,000. The profit is ₹300, so the profit % is $\frac{300}{2000} \times 100$ = (a) 15%.

Question 19

A fruit seller buys 360 bananas at ₹4.50 each and pays ₹180 to bring them to his stall. He sells all of them at ₹6 each. What is his profit percentage? (a) $33\frac{1}{3}\%$ (b) 20% (c) $16\frac{2}{3}\%$ (d) 25%

Answer. CP = 360 × 4.50 + 180 = 1,620 + 180 = ₹1,800, which is ₹5 a banana. SP = 360 × 6 = ₹2,160. The profit is ₹360 on ₹1,800, which is (b) 20%.

Question 20

A tea stall pays ₹750 a day as rent. Each cup of tea costs ₹6 to make and sells for ₹10. How many cups must be sold in a day to make a net profit of ₹650 after paying the rent? (a) 163 (b) 188 (c) 140 (d) 350

Answer. Each cup gives a profit of 10 − 6 = ₹4. The cups must first cover the rent and then earn ₹650, so they must bring in a profit of 750 + 650 = ₹1,400. That needs 1,400 ÷ 4 = (d) 350 cups. Leaving out the rent gives 163 (650 ÷ 4 = 162.5, rounded up).