CAT 2018 [SLOT 1] Quant Question with Solution 29

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. 

It has been given that the profit is 10% if the 2 varieties are mixed in the ratio 3:2

Let the cost price of the mixture be x. 

It has been given that 1.1x = 40

x = 40/1.1

$\frac{3a+2b}{5} = \frac{40}{1.1}$

$3.3a+2.2b=200$ --------(1)

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

$\frac{2a+3b}{5} = \frac{40}{1.05}$

$2.1a+3.15b=200$ ------(2)

Equating (1) and (2), we get, 

$3.3a+2.2b = 2.1a+3.15b$

$1.2a=0.95b$

$\frac{a}{b} = \frac{0.95}{1.2}$

$\frac{a}{b} = \frac{19}{24}$