Question

A merchant has 4500 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He
gains 14% on the whole.
The quantity sold at 18% profit is:
in kg​

Answer 1

The quantity sold at 18 % profit is 2700 kg.

A merchant has 4500 kg of sugar , part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole.

We have to find the quantity sold at 18 % profit.

Method 1 : Mixture and Allegation method :

Let x : y is the ratio of sugar sold at 8 % profit and 18 % profit.

⇒ 8% × x + 18 % × y = 14% × (x + y)

⇒8x + 18y = 14x + 14y

⇒4y = 6x

⇒x/y = 2/3

∴ the quantity sold at 18 % profit = 3/(2 + 3) × 4500 kg = 3/5 × 4500 = 2700 kg

Therefore the quantity of sugar sold at 18 % profit is 2700 kg.

method 2 : Let the quantity of sugar sold at 18 % profit is x kg then the quantity of sugar sold at 8 % profit is (4500 - x) kg.

∴ 18% of x + 8 % of (4500 - x) = 14 % of 4500

⇒18x + 8 × 4500 - 8x = 14 × 4500

⇒10x = 6 × 4500

⇒x = 6 × 450 = 2700 kg

Therefore the quantity of sugar sold at 18 % profit is 2700 kg.