Instructions

For the following questions answer them individually

Question 1

What is the approximate amount on a sum of Rs. 1000 at 15% p.a. compounded thrice a year for a period of 2 years?

Solution

A = P$$(1+r/n)^{nt}$$ where n is the number of times the interest is compounded per year and t is the number of years the principal is borrowed for.
Putting the value, A = 1000$$(1+0.15/3)^{3*2}$$ = Rs 1340 (approx.)

Question 2

Due to inflation, the price of an item increased by 5% in the first month, 10% in the second month, 15% in the third month, 20% in the fourth month and 25% in the fifth month. What is the total percentage increase in the price of the product compared to the initial value?

Solution

Let the initial price be 100k

The price at the end of the first month is 105k. At the end of second month, the price is 115.5k.

At the end of the third month, the price is 132.82k.

At the end of the fourth month, the price is 159.39k, and at the end of the 5th month, it is 199.23k.

So, percentage increase in price = (199.23k - 100k)/100k * 100% = 99.23%

Question 3

Salman is a trader who buys Cashews from Kerala at wholesale rate of Rs.6000 per tin and sells them at 50% higher rate to Delhi shopowners.The Cashews can be sold at the given rate only if they are unbroken.The selling price is reduced by 15% for broken cashews.How much would Salman earn per kg if 25% of the total cashews he sold were broken?(1 tin=11.5kg)

Solution

Let's assume he sold 1 tin of cashews
S.P of cashew if all cashews were unbroken = 9000
S.P of unbroken cashwes = 75% of 9000 = 6750
S.P of broken cashews = [(100-15)(25% of 9000)]/100 = 1912.5
profit for 1 tin cashews = (6750 + 1912.5)-6000 = 2662.5
thus profit per kg = 2662.5/11.5 = Rs 231.52

Question 4

The price of an item is marked at 20% more than its cost price. What is the average of minimum and maximum discount percentage that the seller can offer so that he makes a profit not more than 10% and not less than 5%?

Solution

Let the CP be 100.

MP = 120

SP can be in the range 105 to 110.

Therefore, the discount should be in the range 10-15

=> Minimum discount % = 8.33% and maximum discount % = 12.5%.

Average of these two values = 10.41.

Question 5

The cost price of a pen is Rs. 20. A merchant sells the first pen for Rs. 2, second pen for Rs.4, third pen for Rs.6 and so on. What is the number of pens he should sell to make an overall profit of 20%?

Solution

The total selling price of n pens is 2+4+ . . . +2n = n*(n+1)
The total cost price is 20n
So, n(n+1)= 120%*20n.
Or, n+1=24 and n=23

Question 6

A milk vendor has 3 milk solutions at his disposal. He pays Rs. 6/litre for the first one, Rs. 8/litre for the second and Rs. 10/litre for the third. He then mixed them, respectively, in the ratio 5:4:3 by volume and sold the same to a customer at 50% profit. The price at which he sold to the customer is

Solution

Let the three quantities be 5 l, 4 l and 3 l.

Cost price of the mixture = (5*6 + 4*8 + 3*10)/(5+4+3)

= (30+32+30)/12 = 92/12 = 23/3.

Therefore, selling price = (3/2)*(23/3) = Rs 11.5.

Question 7

A trader bought some rice from a wholesaler. The trader cons him into selling 25% more rice than what he is paying for. While selling, he marks up the price by 20% and offers a discount of 20% to assume certain amount of profit/loss.

This profit/loss is the same as the profit he would have made if he sold all the rice he bought for Rs 'A' per kg. It is also known that 'A' is Rs 4 more than the rate he effectively got the rice for, after conning the wholesaler. What is the price of rice per kg?

Solution

Let the price of 100kg be Rs 100x. This means price per kg is x
Initially the trader buys 125 kg for the price of 100kg rice i.e. for Rs 100x.
Effective cost price per kg for the trader is $$\frac{100x}{125}=0.8x$$

The marked up price is $$x\cdot1.2$$ per kg (20% price markup)
The selling price is $$x\cdot1.2\cdot0.8=0.96x$$ per kg (20% discount)
The total selling price for the trader is $$125\cdot0.96x=120x\ \ \longrightarrow\ \ eqn1$$

Selling price $$'A' = \text{Effective CP} +4 = 0.8x+4$$
Total selling price$$\ =\ 125\cdot A = 125(0.8x+4) = 100x+500\ \ \ \longrightarrow\ \ \ eqn2$$

Since, CP is fixed(100x), and both cases yield the same profits,
we can conclude that their selling prices are same.

Equating 1 and 2, $$120x=100x+500\ \longrightarrow\ \ 20x=500\ \longrightarrow\ \ x=25$$
Thus, the price is Rs 2500 for 100 kg or Rs 25/kg.

Question 8

Sriram, a shopkeeper decides to give huge discounts for shirts and jeans in order to clear his old stock. A person buying 5 shirts is given 3 jeans free and when 9 jeans are bought 3 shirts are given free. Rajesh buys 15 shirts and Belram buys 27 jeans. The overall percentage discount obtained by Rajesh is 25%. What is the percentage discount obtained by Belram on his purchase ? (The price of all the shirts is equal. Also, the price of all the jeans is equal)

Solution

Let the price of a single shirt be x and that of a jean be y.
When Rajesh buys 15 shirts he gets 9 jeans free. Thus, the discount obtained by Rajesh = 9y
Given, the percentage discount obtained by Rajesh = 25%
Thus, $$\frac{9y}{15x + 9y} = 25\% = 1/4$$
On solving we get 9y = 5x
When Belram buys 27 jeans he gets 9 shirts for free. Thus, the discount obtained by Belram = 9x
Thus, the percentage discount obtained by Belram = $$\frac{9x}{27y + 9x}\times100$$% = $$\frac{9x}{15x + 9x}\times100$$% = 37.5%

Question 9

Two shopkeepers sell an item for Rs 100 each. The first shopkeeper calculates the profit on CP and reports his profit percentage to be 25%. The second shopkeeper calculates his profit on SP and reports it to be 25%. How much profit does the second shopkeeper make more than the first?

Solution

The CP of first shopkeeper is Rs 80.

For the second shopkeeper, (100-CP)/100 = 25%.

Therefore, CP = Rs 75.

Therefore, the second shopkeeper makes Rs 5 more than the first shopkeeper.

Question 10

Ram calculates his profit percentage on cost price whereas Shyam calculates his profit percentage on selling price. The difference in their profits is Rs 200. If both of them sell a product at the same price and make 25% profit, find the price at which the product was sold.

Solution

Let the selling price be S.
Profit percentage = 25%
=> Cost price for Ram = (4/5)*S
Profit = S - 4S/5 = S/5

Cost price for Shyam = (3/4)*S
Profit = S - 3S/4 = S/4

S/4 - S/5 = S/20 = 200
=> S = 4000
So, selling price of the product = Rs 4000

Question 11

A cunning shopkeeper buys 110 cm cloth using a faulty meter scale and sells 90 cm cloth using another faulty meter scale. If he sells the cloth at a 10% discount to the cost price, what is his overall profit percentage?

Solution

Assuming the price of cloth is Rs. 100 per meter, the cost price of 110 cm cloth is Rs. 100.
He will sell this 110 cm cloth as 110/90 = 11/9 metres of cloth.
He sells the cloth at Rs. 90 per metre.
Total revenue = (11/9)*90 = Rs. 110
Profit = Rs. 110 - Rs. 100 = Rs. 10.
So profit percentage is 10%

Question 12

A certain number of people take 40 hours to process a fixed quantity of a substance. The substance is priced at Rs x per unit which is determined by the labour costs and other costs. After a new technology is developed, the same number of people take 20 hours to process the same amount of the substance. If the cost of technology is negligible, how much would the new price of the processed substance per unit quantity be? Assume that the other costs remain the same.

Solution

Assuming the quantity as y, the labour cost as L and the other cost as m.

So, $$\ \dfrac{\ L+m}{y}$$ = x

Now, => a+b = x , (Assuming L/y=a and m/y=b)

Since y and m remain the same. Only L is reduced to half.

Then, $$\ \dfrac{a\ }{2}+b$$ = $$\ \dfrac{a\ +b}{2}+\ \dfrac{\ b}{2}$$ = $$\ \dfrac{\ x}{2}+\ \dfrac{\ b}{2}$$ > $$\ \dfrac{\ x}{2}$$

Hence, D is the answer.

Question 13

Ramesh bought some articles at a price which was 10% lower than its marked price. He then sold 50% of the articles at a price 10% above the marked price. After this he sold the next 25% articles at a price which was 20% lower than the marked price. If Ramesh wants to earn a profit of 10% in the entire transaction than at what price should he sell the remaining 25% articles?

Solution

Let’s say that Ramesh bought 100 articles and cost price of each article is Rs 10
So total cost price = 100*10 = 1000
But Ramesh got it for 10% less. So the amount paid by Ramesh = .9*1000 = 900
Now Ramesh wants to earn a profit of 10%, so he must get 900*1.1 = 990 rupees after selling the articles.
He sold first 50 articles for 11 Rs each, so amount earned by him = 50*11 = 550
He sold the next 25 articles at 8 Rs each, so the amount earned by him by selling these 8 articles = 25*8 = 200
So total amount he has earned = 550+200 = 750
He needs to earn 240 Rs more to have an overall profit of 10%.
He has 25 articles so each article has to be sold for Rs 240/25 = 9.6
Since the cost price was 10 this price is 4 % below the cost price.

Question 14

Feroz has two types of grapes- fresh and dry.Fresh grapes contain 90% water and dry grapes contain 25% water. He adds water to the 20 kg dry grapes such that the proportion of water in dry grapes is same as that of fresh grpes. He then sell these grapes at its cost price. Find the profit %age.

Solution

In 20 kg dry grapes, weight of water = 25% of 20 kg = 5kg
Let the water added be x
[5+x]/[20+x] = 9/10
x = 130kg
New weight of grapes = 130+20 = 150kg
Let CP = Re 1/kg
Total CP = Rs 20
Total SP = Rs(130+20) = Rs 150
Profit% = 130/20 = 650%

Question 15

A shopkeeper sells 1 kg rice to two customers Rani and Vani. For Rani he charges exactly the cost price but under weighs the quantity by 10%. For Vani he sells at 20% more than cost price but over weighs the quantity by 10%. What is his overall profit/ loss percentage?

Solution

Let the cost price of 1 kg of rice be C.
For Rani he sells at C but only sells 0.9 kg instead of 1 kg.
For Vani he sells at 1.2C but sells 1.1 kg instead of 1 kg.
Overall he sold 2 kg rice together and the cost price for it is 2C.
His net revenue after both the transactions is C+1.2C = 2.2C
His profit = 0.2C
Profit % = $$ (\frac{0.2C}{2C})\times100$$ = 10% profit.

Question 16

Ram calculates his profit percentage on cost price whereas Shyam calculates his profit percentage on selling price. The difference in their profits is Rs 200. If both of them sell a product at the same price and make 25% profit, find the price at which the product was sold.

Solution

Let the selling price be S.
Profit percentage = 25%
=> Cost price for Ram = (4/5)*S
Profit = S - 4S/5 = S/5

Cost price for Shyam = (3/4)*S
Profit = S - 3S/4 = S/4

S/4 - S/5 = S/20 = 200
=> S = 4000
So, selling price of the product = Rs 4000

Question 17

The difference between compound interest and simple interest on a sum of Rs. 5000 at the end of 3 years is Rs 224.64. Find the rate of interest, if both simple interest and compound interest are calculated at the same rate of interest.

Solution

When the rate of interest is 12%, SI = 5000*3*12/100

In the case of compound interest, Amount = $$P(1+r)^n$$

CI = Amount - P = $$P(1+r)^n - P$$

CI = $$5000(1+12/100)^3 - 5000$$

CI - SI = $$5000(1+12/100)^3 - 5000 - 5000*3*12/100 = 224.64$$

Alternate Method:

Amount = $$P(1+r)^n$$

CI = Amount - P = $$P(1+r)^n - P$$

CI = $$5000(1+r/100)^3 - 5000$$

SI = 5000*3*r/100

CI - SI = $$5000(1+r/100)^3 - 5000 - 5000*3*r/100 = 224.64$$

Let R= r/100

CI - SI = $$5000(1+R)^3 - 5000 - 5000*3*R = 224.64$$

= $$(1+R)^3 - 1 - 3*R = 224.64/5000$$

=$$R^3+ 1+3R^2+3R - 1 - 3*R = 224.64/5000$$

=$$R^3+3R^2 = 224.64/5000$$

Solving the cubic equation we will get R=0.12

r= 12%

Question 18

Fresh and Juicy has 2 juice stalls, one in Bandra and one in Andheri. In Bandra, it sells 10 litres of Apple juice, 10 litres of Banana shake and 10 litres of Chiku shake at 25%, 30%, and 10% profit respectively for Rs 3200. In Andheri, it sells 2 litres of Apple juice, 2 litres of Banana shake and 2 litres of Chiku shake at 40%, 45%, and 25% profit respectively for Rs 718. The cost price of all juices/shakes are same for both stalls. What would be the total selling price if he sells 25 litres of each juice/shake at 15% profit? (Enter ‘-1’ if the answer cannot be determined)

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Solution

Let the cost price of 10 liters of Apple Juice, Banana Shake, and Chiku Shake be a, b, and c
=> 1.25a+1.3b+1.1c = 3200 -(1)
Let’s assume he sold 10 liters of each juice/shake in Andheri as well.
=> 1.4a+1.45b+1.25c= 5 X 718 = 3590 -(2)
Subtracting 1 from 2 we get,
0.15a+0.15b+0.15c = 390
=> a+b+c = 2600

The cost price of 10 liters of Apple Juice, Banana Shake, and Chiku Shake = a+b+c= 2600

The cost price of 25 liter of Apple Juice, Banana Shake, and Chiku Shake is 2600 x 25/10= 6500

Thus, the total selling price of 25 litres of all juice/shake at 15% profit is 1.15 X 6500 = Rs 7475

Question 19

A shopkeeper obtains a profit of 25% on an item by selling it at marked price. If the cost price and the marked price of the product increases by 10%, what discount should the shopkeeper give on the marked price, so that the overall profit comes down to 20% ?

Solution

Let the CP be 100. Profit = 25%

=> The SP = MP = 125.

New CP = 110, new MP = 137.5.

New profit = 20% => New SP = 132.

Therefore, required discount % on MP = (5.5/137.5)*100 = 4%.

Question 20

On a sum of money, the simple interest ( rate of interest r )for 2 years is the same as compound interest ( rate of interest R ) for the same time period. What is the relation between the rates of interest?

Solution

SI = p * 2 * r/100

CI = $$p*(1+R/100)^2-p$$= $$p(2R/100 + (R/100)^2)$$

Since they are equal, $$p * 2 * r/100 = p(2R/100 + (R/100)^2)$$

$$R^2 + 200R - 200r = 0$$

Solving the equation, we get $$R = -100 \pm \sqrt{10000 + 200r}$$

Since, R cannot be negative the only possible value of $$R = -100 + \sqrt{10000 + 200r}$$

=> $$ R + 100 = \sqrt{10000 + 200r}$$

Question 21

Salman is a trader who buys Cashews from Kerala at wholesale rate of Rs.6000 per tin and sells them at 50% higher rate to Delhi shopowners.The Cashews can be sold at the given rate only if they are unbroken.The selling price is reduced by 15% for broken cashews.How much would Salman earn per kg if 25% of the total cashews he sold were broken?(1 tin=11.5kg)

Solution

Let's assume he sold 1 tin of cashews
S.P of cashew if all cashews were unbroken = 9000
S.P of unbroken cashwes = 75% of 9000 = 6750
S.P of broken cashews = [(100-15)(25% of 9000)]/100 = 1912.5
profit for 1 tin cashews = (6750 + 1912.5)-6000 = 2662.5
thus profit per kg = 2662.5/11.5 = Rs 231.52

Question 22

The cost price of a pen is Rs. 20. A merchant sells the first pen for Rs. 2, second pen for Rs.4, third pen for Rs.6 and so on. What is the number of pens he should sell to make an overall profit of 20%?

Solution

The total selling price of the n pens is 2+4+...+2n.

2+4+6+..........2n can be written as 2(1+2+..............n) = 2 (n(n+1)/2) = n(n+1)

As the profit percentage is 20%, it implies that n(n+1) = 120%*20n=24n. Hence, $$n^2=23n$$. Hence, n=23.

Question 23

A certain number of people take 40 hours to process a fixed quantity of a substance. The substance is priced at Rs x per unit which is determined by the labour costs and other costs. After a new technology is developed, the same number of people take 20 hours to process the same amount of the substance. If the cost of technology is negligible, how much would the new price of the processed substance per unit quantity be? Assume that the other costs remain the same.

Solution

Assuming the quantity as y, the labour cost as L and the other cost as m.

So, $$\ \dfrac{\ L+m}{y}$$ = x

Now, => a+b = x , (Assuming L/y=a and m/y=b)

Since y and m remain the same. Only L is reduced to half.

Then, $$\ \dfrac{a\ }{2}+b$$ = $$\ \dfrac{a\ +b}{2}+\ \dfrac{\ b}{2}$$ = $$\ \dfrac{\ x}{2}+\ \dfrac{\ b}{2}$$ > $$\ \dfrac{\ x}{2}$$

Hence, D is the answer.

CAT 2023 Profit, Loss and Interest Questions with Answers

Profit, Loss and Interest

Take a free CAT Mock

What is the approximate amount on a sum of Rs. 1000 at 15% p.a. compounded thrice a year for a period of 2 years?

Due to inflation, the price of an item increased by 5% in the first month, 10% in the second month, 15% in the third month, 20% in the fourth month and 25% in the fifth month. What is the total percentage increase in the price of the product compared to the initial value?

The price of an item is marked at 20% more than its cost price. What is the average of minimum and maximum discount percentage that the seller can offer so that he makes a profit not more than 10% and not less than 5%?

The cost price of a pen is Rs. 20. A merchant sells the first pen for Rs. 2, second pen for Rs.4, third pen for Rs.6 and so on. What is the number of pens he should sell to make an overall profit of 20%?

Two shopkeepers sell an item for Rs 100 each. The first shopkeeper calculates the profit on CP and reports his profit percentage to be 25%. The second shopkeeper calculates his profit on SP and reports it to be 25%. How much profit does the second shopkeeper make more than the first?

Ram calculates his profit percentage on cost price whereas Shyam calculates his profit percentage on selling price. The difference in their profits is Rs 200. If both of them sell a product at the same price and make 25% profit, find the price at which the product was sold.

A cunning shopkeeper buys 110 cm cloth using a faulty meter scale and sells 90 cm cloth using another faulty meter scale. If he sells the cloth at a 10% discount to the cost price, what is his overall profit percentage?

Feroz has two types of grapes- fresh and dry.Fresh grapes contain 90% water and dry grapes contain 25% water. He adds water to the 20 kg dry grapes such that the proportion of water in dry grapes is same as that of fresh grpes. He then sell these grapes at its cost price. Find the profit %age.

A shopkeeper sells 1 kg rice to two customers Rani and Vani. For Rani he charges exactly the cost price but under weighs the quantity by 10%. For Vani he sells at 20% more than cost price but over weighs the quantity by 10%. What is his overall profit/ loss percentage?

Ram calculates his profit percentage on cost price whereas Shyam calculates his profit percentage on selling price. The difference in their profits is Rs 200. If both of them sell a product at the same price and make 25% profit, find the price at which the product was sold.

The difference between compound interest and simple interest on a sum of Rs. 5000 at the end of 3 years is Rs 224.64. Find the rate of interest, if both simple interest and compound interest are calculated at the same rate of interest.

A shopkeeper obtains a profit of 25% on an item by selling it at marked price. If the cost price and the marked price of the product increases by 10%, what discount should the shopkeeper give on the marked price, so that the overall profit comes down to 20% ?

On a sum of money, the simple interest ( rate of interest r )for 2 years is the same as compound interest ( rate of interest R ) for the same time period. What is the relation between the rates of interest?

The cost price of a pen is Rs. 20. A merchant sells the first pen for Rs. 2, second pen for Rs.4, third pen for Rs.6 and so on. What is the number of pens he should sell to make an overall profit of 20%?

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