Profit, Discounts, List Price Question - XAT 2020 / TANCET 2020

The question given below is a sample practice problem in Profits, Discounts and Markup. It is an Arithmetic Topic and the problem provides an understanding of the core concept related to profits and discounts.

Question

If a merchant offers a discount of 30% on the list price, then she makes a loss of 16%. What % profit or % loss will she make if she sells at a discount of 10% of the list price?

1. 6% loss
2. 0.8% profit
3. 6.25% loss
4. 8% profit

Correct Answer - 8% profit. Choice (4)

Explanatory Answer

Let the cost price of the article be Rs.100.
Let the List price of the article by "x".

Then, when the merchant offers a discount of 30%, the merchant will sell the article at x - 30% of x = 70% of x = 0.7x. .......(1)
Note: Discount is measured as a percentage of list price.

The loss made by the merchant when she offers a discount of 30% is 16%.
Therefore, the merchant would have got 100 - 16% of 100 = Rs.84 when she offered a discount of 30%. .......(2)
Note: Loss is always measured as a percentage of cost price.

Therefore, equating equations (1) and (2), we get
0.7x = 84
or x = 120.

If the list price is Rs.120 (our assumption of cost price is Rs.100), then when the merchant offers a discount of 10%, she will sell the article at
120 - 10%o of 120 = Rs.108.

As the cost price of the article was Rs.100 and the merchant gets Rs.108 while offering a discount of 10%, she will make a profit of 8%.

Correct answer choice (4)