Profit, loss, and interest is one of the most important topics for CAT. The topics covered are successive percentage changes, fraudulent shopkeepers and faulty balances, simple and compound interest. Solve the profit and loss questions given below and go through the detailed explanations to understand this topic.

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Instructions

For the following questions answer them individually

Question 1

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.

Question 2

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?

Question 3

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% ?

Question 4

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?

Question 5

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.

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

Question 7

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%?

Question 8

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?

Question 9

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%?

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.

Question 11

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.

Question 12

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)

Question 13

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.

Question 14

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)

Question 15

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?

Question 16

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?

Question 17

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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Question 18

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%?

Question 19

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?

Question 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?

Question 21

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?

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