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# Profit Loss and Interest Questions for CAT

Profit and Loss is one of the important topics in the CAT Quants section. Over the past few years, CAT Profit and Loss questions have made a recurrent appearance in the Quant section. You can expect around 1-2 questions in the new format of the CAT Quant section. If you’re new to this section, you can check out the CAT Profit and Loss Questions from the CAT Previous Year papers. In this article, we will look into some very important Profit and Loss questions PDF(with solutions) for CAT. You can also download these CAT Profit and Loss questions with detailed solutions, which also include important tricks to solve these questions.

Question 1: A man borrows Rs 4000 at 15% compound interest. At the end of each year he pays back Rs 1500. How much amount is required to pay at the end of third year to clear all his dues :

a) Rs.775.75

b) Rs.973.85

c) Rs.1500

d) Rs.874.75

Solution:

Time value of money Rs 4,000 at the end of 3 years = 4,000$\left(1\ +\ \frac{15}{100}\right)^3$ = Rs 6083.5

Value of first installment at the end of 3 years = 1500$\left(1\ +\ \frac{15}{100}\right)^2$ = Rs 1983.75

Value of second installment at the end of 3 years = 1500$\left(1\ +\ \frac{15}{100}\right)$ = Rs 1725

Value of third installment = 1500

Let us assume he has to pay Rs. x to clear all his dues

1983.75 + 1725 + 1500 + x = 6083.5

x = Rs 874.75

Question 2: If the cost price is 80% of the selling price, then what is the profit in percentage?

a) 20%

b) 25%

c) 16%

d) 22.5%

Solution:

Given, cost price is 80% of selling price

C.P = 0.8 S.P

Profit = $\ \frac{\ S.P\ -\ C.P}{C.P}\times\ 100$

= $\ \frac{\ S.P\ -\ 0.8S.P}{0.8S.P}\times\ 100$

=$\ \frac{0.2}{0.8}\times\ 100$

= 25%

Question 3: If the cost price of 20 articles is equal to the selling price of 25 articles, then the
percentage profit or loss made is_______.

a) 20% profit

b) 25% loss

c) 25% profit

d) 20% loss

Solution:

Let the cost price of one article be C.P and selling price of one article be S.P

It is given that,

20C.P = 25S.P

Loss% = $\ \frac{\ C.P-S.P}{C.P}\times100$ = $\ \ \frac{\ \frac{5}{4}S.P-S.P}{\frac{5}{4}S.P}\times\ 100\$ = 20%

Question 4: Shankar Fertilizer Limited and Shah Fertilizer Limited purchased one packet of Phosphorus each at the same price. Later on GreenP Company purchased both the packets at equal price from Shankar Fertilizer Limited and Shah Fertilizer Limited. But the profit percentage of Shankar Fertilizer Limited was $X$ while that of Shah Fertilizer Limited was $Y$. Shah Fertilizer Limited calculated his profit on the selling price. Thus $Y=45\frac{9}{20}\%$. If the GreenP 20 Company sells one of the packets to Mehrauli Nursery at $X\%$ profit, then what is the cost price for Mehrauli Nursery. while GreenP Company purchased each of the Phosphorus packets at Rs. 330?

a) 726

b) 762

c) 526

d) 584

Solution:

Shankar’s profit% = $\frac{P}{C.P}\times\ 100$ = X
Shah’s profit% = $\frac{P}{S.P}\times\ 100$ = Y
$\ \frac{\ S.P}{C.P}=\frac{X}{Y}$
It is given,
$Y\ =\ \frac{909}{2000}X$
$\frac{X}{Y}\ =\ \frac{2000}{909}$
$\frac{S.P}{C.P}\ =\ \frac{2000}{909}$
$\frac{P}{C.P}\ =\ \frac{1091}{909}$
It is given,
C.P = Rs 330
Profit $P\ =\ \frac{1091}{909}\times\ 330\ \approx\ 396$
The cost price for Mehrauli Nursery = 396 + 330 = Rs 726

Question 5: Same item is sold for Rs. 600 and Rs. 175, respectively. The profit earned on the first sale is 20times the loss incurred on the second sale. To make an overall profit of 30% in the whole transaction, atwhat price the second sale should happen:

a) Rs. 310 approx

b) Rs. 238 approx

c) Rs. 254 approx

d) Rs. 357 approx

Solution:

Let the CP be x

Now as per question, $600-x=20\left(x-175\right)$

21x = 4100

x= 195.24

Therefore, to make a profit of 30% selling price of second article should be = $1.3\times\ 195.24\ =\ 253.81$

Question 6: If a principal P amounts to A in two years when compounded half yearly with r% interest. The same principal P amounts to A in two years when compounded annually with R% interest, then which of the following relationship is true?

a) $r > R$

b) $r = R$

c) $r < R$

d) $r \leq R$

Solution:

Since in first case we are compounding half-yearly and in second case we are compounding yearly and the amount received and the principal invested in both the cases is same so interest rate in the first case is lower than the interest rate in the second case.

Question 7: Bank A offers 6% interest rate per annum compounded half-yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

a) 3436

b) 2436

c) 2346

d) 1436

Solution:

Bank A: 6% p.a. 1/2 yearly (CI)

Bank B: x% p.a (SI)

Bank C: 2x% p.a (SI)

Let Raju invest Rs P in bank B for t years. Hence, Rupa invests Rs 10,000 in bank C for 2t years.

Now,

$P\left(\frac{x}{100}\right)t\ =\ P\left(1+\frac{3}{100}\right)^2-P$

$\left(\frac{x}{100}\right)t\ =\ 1.0609-1$

$\left(\frac{x}{100}\right)t\ =\ 0.0609$

We need to calculate

SI = $10000\times\ 2t\times\ \left(\frac{2x}{100}\right)=40000\left(\frac{x}{100}\right)t=40000\times\ 0.0609=2436$

Question 8: Anil, Bobby, and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil’s share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu’s share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is

a) 2000

b) 2400

c) 2200

d) 1800

Solution:

Let the amount invested by Anil Bobby and Chintu be x, y, and z.

Considering x+y+z = 100*p.

Given Anil’s share was 70 percent = 70*p.

As per the information provided :

His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%.

Since the profits are distributed in the ratio of their investments :

With a 3% decrease in the profits the value of profit earned by A decreased by Rs 420 which was 70 percent of the total invested.

Hence for all three of them would be combinedly losing $\left(420\right)\cdot\left(\frac{10}{7}\right)\ =\ 600$

Hence 3 percent profit was equivalent to  Rs 600.

The initial investment is equivalent to Rs 20000.

This is the total amount invested.

Chintu’s profit share increased by Rs 80 when the profit percentage increased by 2 %. A 2 percent increase in profit is equivalent to Rs 20000*2/100 = Rs 400.

Of which Rs 80 is earned by Chintu which is 20% of the total Rs 400.

Hence he invested 20% of the total amount.

Bobby invested the other 10 percent.

10 percent of Rs 20000 = Rs 2000

Question 9: The ratio of simple interest calculated biennially and quarterly at the same rate ofinterest for the same time period is _____.

a) 1 : 4

b) 2 : 1

c) 1 : 2

d) 4 : 1

Solution:

Simple Interest biennially = (1/2)*(P*r*2T)/100 = PrT/100

Simple Interest quarterly = (8)*(P*r*T/4)/100 = 2PrT/100

So, Ratio = 1:2

Question 10: The least number of complete years in which a sum of money will be more thandoubled at 10% compound interest is ________.

a) 10

b) 8

c) 5

d) 6

Solution:

No. of years in which a sum of money invested at r% compounded annually amounts to double is 72/r years

So, no. of years in which the amount will be doubled = 72/10 = 7.2 years

So, the least no. of years for which the amount will be more than doubled will be 8 years.

Question 11: An article when sold for 960 fetches 20% profit.What would be the percent profit /loss if such 5 article are sold for Rs. 825/-each?

a) 3.125 % profit

b) 3.125 % loss

c) Neither profit nor loss

d) 16.5 % profit

e) None of these

Solution:

Let cost price of an article = $Rs.$ $100x$

If Selling price = Rs 960

=> Profit % = $\frac{960-100x}{100x} \times 100=20$

=> $960-100x=20x$

=> $20x+100x=120x=960$

=> $x=\frac{960}{120}=8$

Thus, cost price of 1 article = $100 \times 8 = Rs.$ $800$

If selling price = Rs. 825

$\therefore$ Profit % = $\frac{825-800}{800} \times 100$

= $\frac{25}{8} = 3.125\%$

=> Ans – (A)

Question 12: An item was bought at Rs. X and sold at Rs. Y, there by earning a profit of 20%. Had the value of X been 15% less and the value of Y been Rs. 76 less, a profit of 30% would have been earned. What was the value of ‘X’

a) Rs. 640

b) Rs.400

c) Rs.600

d) Rs.800

e) Rs.840

Solution:

C.P. = $Rs. x$

S.P. = $Rs. y$

Profit % = $\frac{y – x}{x} \times 100 = 20$

=> $\frac{y – x}{x} = \frac{20}{100} = \frac{1}{5}$

=> $5y – 5x = x$ => $6x = 5y$

=> $y = \frac{6 x}{5}$ ———–(i)

If, value of X been 15% less and the value of Y been Rs. 76 less

=> $x’ = \frac{85}{100} \times x = \frac{17 x}{20}$

=> $y’ = y – 76$

Profit % = $\frac{y’ – x’}{x’} \times 100 = 30$

=> $\frac{(y – 76) – (\frac{17 x}{20})}{\frac{17 x}{20}} = \frac{30}{100} = \frac{3}{10}$

=> $10 \times [(y – 76) – (\frac{17 x}{20}] = 3 \times \frac{17 x}{20}$

=> $10y – 760 – \frac{170 x}{20} = \frac{51 x}{20}$

=> $10y – \frac{221 x}{20} = 760$

Using, equaiton (i), we get :

=> $(10 \times \frac{6 x}{5}) – \frac{221 x}{20} = 760$

=> $12x – \frac{221 x}{20} = 760$

=> $\frac{19 x}{20} = 760$

=> $x = 760 \times \frac{20}{19}$

=> $x = 40 \times 20 = Rs. 800$

Question 13: Shri Ramlal purchased a TV set for Rs. 12,500 and spent Rs. 300 on transportation and Rs. 800 on installation. At what price should he sell it so as to earn an overall profit of 15% ?

a) Rs. 14,560

b) Rs. 14,375

c) Rs. 15,460

d) Rs. 15,375

e) None of these

Solution:

Cost price of TV = Rs. 12,500

Amount spent on transportation = Rs. 300 and installation = Rs. 800

Net spent = Rs. (12500 + 300 + 800) = Rs. 13,600

Let selling price = $Rs.x$

Profit % = $\frac{x-13600}{13600} \times 100=15$

=> $x-13600=15 \times 136$

=> $x=2040+13600$

=> $x=Rs.$ $15,640$

=> Ans – (E)

Question 14: A trader sells an item to a retailer at 20% discount, but charges 10% on the discounted price, for delivery and packaging. The retailer sells it for Rs. 2046 more, thereby earning a profit of 25%. At what price had the trader marked the item?

a) Rs. 9400

b) Rs. 9000

c) Rs. 8000

d) Rs. 12000

e) Rs. 9300

Solution:

Let Marked price of item = $Rs. 100x$

=> Selling price of trader = Cost price of retailer = $100x \times \frac{80}{100} \times \frac{110}{100}$

= $Rs. 88x$

Selling price of retailer = $Rs. (88x + 2046)$

Profit % = $\frac{(88x + 2046) – 88x}{88x} \times 100 = 25$

=> $\frac{2046}{88x} = \frac{25}{100} = \frac{1}{4}$

=> $x = \frac{2046 \times 4}{88} = 93$

$\therefore$ Marked price = $100 \times 93 = Rs. 9,300$

Question 15: A starts a business with Rs. 2500. After one month from the start of the business, B joined with Rs. 4500 and A withdrew completely after eleven months from the start of the business. If the difference between A’s and B’s respective shares in the annual profit was Rs. 4800, what was the annual profit earned?

a) Rs. 14800

b) Rs. 16800

c) Rs. 14400

d) Rs. 11400

e) Rs. 15600

Solution:

Amount invested by A = Rs. 2500 and by B = Rs. 4500

Both invested for 11 months.

Ratio of profit shared by A and B

= $(2500 \times 11) : (4500 \times 11)$

= $5 : 9$

Let total profit earned by A and B respectively = $Rs. 5x$ and $Rs. 9x$

=> $9x – 5x = 4800$

=> $x = \frac{4800}{4} = 1200$

$\therefore$ Total profit = $9x + 5x = 14x$

= $14 \times 1200 = Rs. 16,800$

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