Question

A merchant has 2000 kg of rice, one part of which he sells at 36% profit and the rest at 16% profit. he gains 28% on the whole. find the quantity sold at 16%.

Answer 1

Let the cost price per kg be x.

The cost price of 2000kg will be :

2000x

If it is sold at a gain of 28% the selling price will be :

1.28 × 2000x = 2560x

Let the quantity sold at 36% profit be y then the quantity sold at 16% gain is 2000 - y.

The cost of quantity y is :

= xy

The selling price is :

= 1.36xy

The cost price of 2000 - y is :

x(2000 - y) = 2000x - xy

The selling price is :

1.16(2000x - xy) = 2320x - 1.16xy

The total selling price for the two quantities is :

2320x - 1.16xy + 1.36xy = 2320x + 0.2xy

2320x + 0.2xy = 2560x

0.2xy = 240x

y = 240x/0.2x

y = 1200

The quantity sold at 16% gain is :

2000 - 1200 = 800kgs

= 800kgs