Ratio Proportion

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

  1. 18 : 25
  2. 19 : 24
  3. 21 : 25
  4. 17 : 25

Answer

The selling price of the mixture is Rs. 40/kg.

Let a be the quantity of tea A in the mixture and b be the quantity of tea B in the mixture. 

The profit is 10% if the two varieties are mixed in the ratio 3 : 2.

Let the cost price of the mixture be x. 

So, 1.1x = 40

x = 40/1.1

(3a + 2b)/5 = 40/1.1

3.3a + 2.2b = 200

The profit is 5% if the two varieties are mixed in the ratio 2 : 3.

(2a + 3b)/5 = 40/1.05

2.1a + 3.15b = 200

Equating both the equations, we get

3.3a + 2.2b = 2.1a + 3.15b

1.2a = 0.95b

a/b = 0.95/1.2

a/b = 19/24

The correct option is B.