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

A shrewd trader bought some rice. But while buying rice from a wholesaler, he cons him into selling 25% more rice than what he is paying for. He marks up the price by 20% and after giving a discount of 20% makes some profit/loss. This profit/loss is same as the profit he would have made if he sold all the rice he bought at 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 2

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 3

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 ). What is the relation between the rates of interest?

Question 4

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 5

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 6

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 7

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 8

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

Question 9

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 10

It takes 40 men 40 hours to work on processing a rare substance X, and it is priced at x per unit quantity. A new technology was developed using which 40 men can now process the same quantity in 20 hours. If the cost of technology is negligible, how much would the new price of the processed substance per unit quantity be?

Question 11

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 12

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 13

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 14

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 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?

Question 16

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 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

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 19

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 20

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.

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