Question

A trader has 280 l of oil, a part of which he sells at a profit of 18% and the rest at 10% loss. he gains 14% on the whole. what is the quantity sold at 10% loss?

Answer 1

Let the cost price of a litre be x.

The cost of 280l is :

280 × x = 280x

The selling price at 14% gain :

= 1.14 × 280 = 319.2x

Let the quantity sold at a loss of 10% be y then the quantity sold at a gain of 18% be 280 - y

The cost price of quantity y :

= xy

The selling price :

= 0.9xy

The buying price of 280 - y:

= x(280 - y) = 280x - xy

The selling price :

(280x - xy) 1.18

330.4x - 1.18xy

The total selling price for the two quantities is :

330.4x - 1.18xy + xy = 330.4x - 0.18xy

330.4x - 0.18xy = 319.2x

-0.18xy = - 11.2x

y = 11.2x/0.18x

y = 62.2 litres

Quantity sold at a loss of 10% is 62.2 litres.