Question 4 the day : April 3, 2006

The question for the day is a sample practice problem in profit, loss, discounts, an Arithmetic Topic and the problem provides an understanding of the different terms such as Cost Price, List Price, Selling price and margins.

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%.

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