Questions on Profit Loss and Discount has started featuring regularly in CAT quant section. Approximately 3-4 questions are based directly or indirectly in the basic concepts of profit and loss. Various shortcut formulas and tricks are used to solve these questions.

We have selected around 25 types of **questions with solutions from profit and loss** which regularly appear in CAT exam. A student must pay good attention to the approach employed to solve them.

### Quick Tips:

- Get a good grip on the concepts and formulas of percentages.
- Conversion of ratio to percentages and vice versa is very handy simplifying the problems
- There are different varieties of questions from profit loss and discount. Many of the questions have direct formula or tricks. Learn to use them as and when required.
- Remember, Profit is calculated over Cost Price and Discount is calculated over Marked Price.

### Practice Questions

**Question 1:**I sell 16 sheep at a gain of 12.5% and 20 more at a certain gain percent. If 1 gain 25% on the whole, how much percent gain did I make on the latter number?

- 20%
- 25%
- 30%
- 35%

On the whole I gain 25%

Therefore, I should get the cost price of \(36 \times \frac{{125}}{{100}} = 45\) sheep.

But I sell the first lot at a gain of 12.5%

Hence by selling 16 sheep, I get the cost price of \(16\times \frac{112.5}{100}=18\) sheep.

Therefore, I should get the cost price of 45-18=27 sheep by selling the second lot of 20. Hence my gain there should be \(\frac{7}{20}\times 100=35%$\)

**Question 2:**A farmer buys 240 cows. He sells some of them at a gain of 20% and the remaining at a gain of 30%. If he gains 28% on the whole, then how many did he sell at a gain of 20%?

- 40
- 48
- 54
- 28

Let him sell x cows at the gain of 20% and y cows at a gain of 30%.

Therefore, 0.2x + 0.3y = -0.28(x+y)

=> y=4x, Therefore, x+4x=240 =>x=48.

**Question 3:**A dealer sells a horse for Rs.400, making a profit of 25%. He sells a second horse at a loss of 10% and on the whole makes neither profit nor loss. What did the second horse cost him?

- Rs.100
- Rs.600
- Rs.800
- Rs.400

In the given question "The dealer sells two horses, one for Rs.400, making a profit of 25% and the other horse at a loss of 10% and makes neither profit nor loss on the whole."

Let the cost price of second horse = Rs.x i.e., 320 + x = 400 + 9x/10 ( since 400 x 100/125 = 320) => x = Rs.800. Ans.(3)

**Question 4:**I buy two horses, A and B. A costs Rs.50 more than B. I sell A at a profit of 16% and 13 at a profit of 7%. My total gain is Rs.100. What was the original price of 8?

- Rs.450
- Rs.400
- Rs.350
- Rs.500

A = B + 50 ….(1)

1.16 A + 1.07 B = A + B + 100 …..(2)

=> A = Rs.450, B = Rs.400. Ans.(2)

**Question 5:**If toffees are bought at the rate 18 for a rupee, then how many of them must be sold for a rupee to gain 20%?

- 14
- 15
- 16
- 12

18 x 100 p = 120x => x = 15. Ans.(2)

**Question 6:**A man's petrol bill in July is Rs.200. In August, the price of petrol increases by 10% and his consumption is reduced by 10%. Find his petrol bill in August.

- Rs.190
- Rs.210
- Rs.200
- Rs.198

Let the consumption in July = x litres,

Therefore, price of petrol = Rs. 200/x

=> Petrol bill in August = (0.9x) x(1.10)x 200/x= Rs.198. Ans.(4)

**Question 7:**I sell a table for Rs.24 and thus make a percentage of profit equal to the cost price. What did the table cost me?

- Rs.10
- Rs.20
- Rs.40
- Rs.30

Let the cost price and profit be X.

Therefore, \(\frac{S.P.-C.P.}{C.P.}\times 100=\Pr ofit%\)

\(\begin{array}{l} = \frac{{24 - x}}{x} \times 100 = x\\ = > {x^2} + 100x - 2400 = 0\\hence\;x = 20\end{array}\)**Question 8:**A bike costs Rs.48000. Its value depreciates by 30% in the first year and in each subsequent year the depreciation is 20% of the value at the beginning of that year. The value of the bike after 3 years will be

- Rs.21504
- Rs.26880
- Rs.38400
- Rs.39480

The required value of the bike after 3 years = \(48000\left( {\frac{{70}}{{100}}} \right){\left( {\frac{{80}}{{100}}} \right)^2} = Rs.21504\)

**Question 9:**A person sold his watch for Rs.75 and got a percentage of profit equal to the cost price. The cost price of the watch is

- Rs.40
- Rs.50
- Rs.35
- Rs.45

Let x be the cost price of the watch.

Therefore, profit percentage is also x.

\(\begin{array}{l}x + x \times \frac{x}{{100}} = 75\\Or\;x = 50\end{array}\)**Question 10:**A man sells two horses for Rs.1955 each. On one he gains 15% and on the other he loses 15%. His total gain or loss is

- Rs.40.00
- Rs.90.00
- Rs.97.75
- Rs.19.55

Loss = 15 x 15/100 = 2.25%.

C.P = (2 x 1955 x 100)/97.75 = Rs.4000.

Loss = 4000 — 2 x (1955) = Rs.90. Ans.(2)

**Question 11:**Vivek bought 5 dozen apples at the rate of Rs.15 per dozen. He spent Rs.15 on transportation. If he sold the apples at the rate of Rs.24 per dozen, what was his profit percentage?

- 25%
- 30%
- 33.33%
- 60%

The Cost Price (C.P) of 1 dozen apples = Rs.15.

Hence, the C.P of 5 dozen apples = 15 x 5 = Rs.75.

Adding Rs.15 towards transportation cost, the total cost price of 5 dozen apples becomes Rs.90.

Now, the Selling Price (S.P) of 1 dozen apples = Rs.24.

Hence, the Sales Revenue of 5 dozen apples = 24 x 5 = Rs.120.

Thus, Net Profit = Sales Revenue - Cost Price = 120 - 90 = Rs.30.

The Profit is always expressed as a percentage to cost price. Required answer = (30/90) x 100 = 33.33%. **Ans.(3)**

__Short-cut:__ Cost of 5 dozen of apples including transportation charges = 15 + (15/3) = Rs.18.

Percentage profit = [(24-18)/18] x100=33.33% .

**Question 12:**A shopkeeper purchases several articles at the rate of 11 for Rs.10 and sells them at the rate of 10 for Rs.11. What would be the profit earned by him?

- 11%
- 10%
- 20%
- 21%

Cost Price for 11 articles = Rs.10 .... (I)

Sales Price for 10 articles = Rs.11 .... (II)

Sales Price for 11 articles = Rs.12.1 (III)

Thus, required profit = [(12.1-10)/10] x 100 = 21%. Ans.(4)

**Question 13:**The cost price of 12 articles is the same as the selling price of 8 articles. What is the profit percent?

- 25%
- 40%
- 50%
- 200%

We have, Cost Price of 12 Numbers = Sales Price of 8 Numbers. In order to arrive at the profit percentage. we need to compare the cost price/ sales price of equal number of articles.

Thus, let C.P of 12 Numbers = S.P of 8 Numbers. = Rs.100.

Hence, S.P of 12 Numbers = 12 x 100 ± 8 = Rs.150.

Thus, Profit = 150 - 100 (for 12 Numbers) = Rs.50.

Therefore Profit percent = (Profit ÷C.P) x 100 = 50%. Ans.(3)

**Alternatively, **

Cost price of 12 Numbers = Selling price of 8 Numbers

=> Selling price of 8 Numbers = Cost price of 8 Numbers + Cost price of 4 Numbers

Therefore, Profit = Cost price of 4 Numbers

=> Profit % =(Cost price of 4 numbers/cost price of 8 numbers)x100=(4/8)x100=50%

**Question 14:**In order to increase revenue, a dealer announces 20% reduction in the unit price of an article. As a result, his sales volume increases by 20%. What is the overall gain/loss to the dealer?

- no profit no loss
- 4% loss
- 10% profit
- Cannot be determined since selling price is unknown

When the two figures of (i) reduction and (ii) increase are same (here, 20% each), the calculation is direct, as follows: (a) Overall gain or loss

=> Always loss. (b) Numerical Values? = 20% x 20% = 4% (multiply two values and divide by 100). Ans.(2)

**Question 15:**Rakesh bought 20 chairs for Rs.1000. He repaired and sold them at the rate of Rs.500 per pair. He got profit of Rs.100 per chair. How much did he spend on repairs?

- Rs.1500
- Rs.2000
- Rs.2500
- Rs.1800

Purchase price for 20 chairs=Rs. 1000

Repairs amount (to be determined) =Rs. X

Sales price for 20 chairs = Rs. 5000

Profit derived for 20 chairs = Rs. 2000

We have, (3) - [(1) + (2)] = (4).

? 5000 - (1000 + X) = 2000 => X = 2000. Ans.(3)

**Question 16:**Kiran buys an article with 25% discount on the marked price. He makes a profit of 10% by selling it at Rs.660. What was the marked price?

- Rs.900
- Rs.600
- Rs.700
- Rs.800

Let the marked price of the article be Rs. X

? Purchase Price (C.P) for Kiran = 0.75 X.

? S.P for Kiran = (0.75 X) + 10% of (0.75 X) = 660.

? 0.825 X = Rs.660 = X = Rs.800. Ans.(4)

**Question 17:**A dishonest dealer pretends to sell at the cost price but earns a profit of 25% by under weighing. What weight must he be using for 1 kg?

- 750 gm
- 800 gm
- 500 gm
- 875 gm

Let the false weight be x gm.

Thus, the profit made is through sale of (100-x) gm

Hence, we have, \(\frac{{100 - x}}{x} = 25\% = > x = 800gm\)

**Question 18:**A' sold a house to Bat a gain of 10% and B sold it to Cat a gain of 20%. If C paid Rs.264000 for it, at what price must A have purchased it

- Rs.200000
- Rs.220000
- Rs.240000
- Rs.250000

Let the cost price for ‘A’ be Rs. X

Therefore, \(\begin{array}{l}x \times \frac{{110}}{{100}} \times \frac{{120}}{{100}} = 264000\\ = > x = 200000\end{array}\)

**Question 19:**An increase, in the cost price of an article, by 22% leads to the value of Rs.61. What was the original cost price of the article?

- Rs.40
- Rs.45
- Rs.50
- Rs.55

Let the original cost price of the article be Rs.'X'. Thus, we get, X + 22% of X = 61 => X = Rs.50. Ans.(3)

**Question 20:**When certain quantity of sugar is sold at Rs.11 per kg, the gain is 10%. If the total gain is Rs.50, what is the quantity of sugar sold?

- 100 kg
- 60 kg
- 50 kg
- 80 kg

The Unit Cost Price of sugar = 11 ÷ 1.1 = Rs.10 per kg.

Thus, by selling one kg, the gain is Re.1.

Hence, when the total gain is Rs.50, 50 kg of sugar must have been sold. Ans.(3)

**Question 21:**What is the cost price of an article, if a loss of 16% is incurred by selling it for Rs.168?

- Rs.200
- Rs.180
- Rs.220
- Rs.210

Let the cost price of the article be Rs. 'X'. Thus, we get, X — (16% of X) = Rs.168 = X = Rs.200. Ans.(1)

**Question 22:**Two successive discounts of 30% and 25% are equivalent to a single discount of

- 45%
- 55%
- 47.50%
- 52.50%

Required discount = 100 — (0.7 x 0.75 x 100) = 47.5%. Ans.(3)

**Question 23:**A man buys two goats at Rs.120 each. He sells one at 25% gain and the other at 25% loss. How much is his profit or loss?

- 6.25% gain
- No loss no gain
- 6.25% loss
- Cannot be determined

As gain or loss is on the cost price.

25% loss on Rs.120 = 25% gain on Rs.120.

As such there is no loss no gain. Ans.(2)

**Question 24:**By what percent should the cost price of an article be marked up such that even after allowing a discount of 50%, a profit of 50% is made?

- 300
- 500
- 100
- 200

Let the Cost Price and Marked Price of the item be Rs. 'X' and 'Y' respectively. Thus, we get, Y — 50% of Y = X + 50% of X 0.5Y = 1.5X. or Y ÷ X = 1.5 ÷ 0.5 = 3.

Thus, the marked price should be 3 times the cost price. Hence, required percentage is 200. Ans.(4)

**Question 25:**A dealer offers three successive discounts of 50%, 20% and 10% on an article. What is the single effective discount rate?

- 60%
- 62%
- 63%
- 64%

Effective discount = 100 — ( 0.5 x 0.8 x 0.9 x 100) = 64%. Ans.(4)