XAT 2015 Quant & DI: Profit Loss

This question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. A total of 33 questions appeared in this section in XAT 2015. This one is a medium level difficulty question and tests the concept of computing percentage of profit. Such questions appear in the aptitude / quant section of CAT, TANCET, GMAT, and GRE.

Question

The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

1. 31%
2. 22%
3. 15%
4. 13%
5. 11%

  Correct Answer      Choice D. The profit percentage is 13%.

Explanatory Answer

Key Data

1. The MRP of the product is 55% above its manufacturing cost.
2. The retailer sells the product after offering a discount of 10% on the MRP.
3. The retailer makes a 23% profit on his purchase price.

Useful Assumption

In Profit Loss questions where all data is given in percentage terms, assume cost price to be 100.
  Let the manufacturing cost = 100

The MRP of the product is 55% above its manufacturing cost
  The MRP of the product = 100 + 55% of 100 = 155.

The retailer sells the product after offering a discount of 10% on the MRP
  So, the retailer sells the product at 155 – 10% of 155 = 155 – 15.5 = 139.5

The retailer makes a 23% profit on his purchase price
Let the purchase price for the retailer be x.
  So, the retailer sells the product at x + 23% of x = 123% of x.

Step to retailer sells the product @ 139.5 = 123% of x
1.23x = 139.5
(or) x = \\frac {139.5} {1.23}\\)
Therefore, x = 113.4

x is the purchase price for the retailer.
So, x has to be selling price for the manufacturer.
The manufacturer sold the product at 113.4.

Cost to the manufacturer is 100.
So, profit made by the manufacturer is 13.4.
Because we assumed the cost price to be 100, the manufacturer makes a 13.4% profit.

Rounded to the nearest integer, it is 13%

  The correct answer is Choice D.

Video Explanation