Problems on Profit and Loss

Profit and Loss is an essential part of Business Mathematics. From the CAT point of view these problems involve a lot of calculations and hence are time consuming. Students should look at the various kinds of problems that can be built on and around this concept.
Let us go through the following examples and apply the concepts learnt in this topic.

Example 1

A banana seller buys bananas at a price of Rs 10 per dozen and sells all of them during the day in bunches of five, charging Rs 7 per bunch. What is his rate of profit?

Solution 

As in the previous example, the exact number of bananas is irrelevant for calculating the profit percentage. It is convention to take the number of bananas to be 60, the least common multiple of 5 and 12.

The cost of sixty bananas is Rs 50 (five dozens at the rate of Rs 10 per dozen) and the revenue from selling them is Rs 84 (twelve bunches at the rate of Rs 7 per bunch).

The profit rate is equal to

Example 2   

A car dealer buys a 1996 model small car and sells it the next day for sixty thousand rupees, after doing a minor painting job costing one thousand rupees. If he earned 20% profit on the deal,what was the purchase price?

Solution  

Let the purchase price of the car for the dealer be Rs x.

His total cost is x + 1000

From the formula for profit we have,

Solving this, we get the purchase price x to be Rs 49,000.

Example 3   

The cost or purchase price of two items is the same. If one of them is sold at a loss of a% and the other at a profit of a%, what is the overall profit?

Solution   
Let the common purchase price be x. Total cost is 2x.
The selling price of the first item is and that of the second item is Adding these two, we see

that the total revenue is also 2x.

Hence, the overall profit is zero. 

Example 4

The selling price of two items is the same, say Rs x. If one of them is sold at a loss of a% and the other at a profit of a%, what is the overall profit of loss (in rupees) from selling these two items? Also calculate the rate of profit or loss.  

Solution
Total revenue is2x
The cost price of the first item is and that of the second item is

Adding these two and simplifying, we see that the total cost is: 

It is obvious that the cost is more than the revenue and the seller makes a loss.

The overall loss for the seller is the difference between the total cost and the total revenue and is equal to: rupees.

The loss rate is. For example, if a = 20%, the rate of overall loss is