CAT 2018

Slot 1

QA

Question & Solution

The selling price of the mixture is Rs.40/kg. 
Let a be the price of 1 kg of tea A in the mixture and b be the price per kg of tea B. 
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
Price per kg of the mixture in ratio 3:2 = $\frac{3a+2b}{5}$
$\frac{3a+2b}{5} = \frac{40}{1.1}$
$3.3a+2.2b=200$ --------(1)

The profit is 5% if the 2 varieties are mixed in the ratio 2:3.
Price per kg of the mixture in ratio 2:3 = $\frac{2a+3b}{5}$
$\frac{2a+3b}{5} = \frac{40}{1.05}$
$2.1a+3.15b=200$ ------(2)

Equating (1) and (2), we get, 
$3.3a+2.2b = 2.1a+3.15b$
$1.2a=0.95b$
$\frac{a}{b} = \frac{0.95}{1.2}$
$\frac{a}{b} = \frac{19}{24}$

Therefore, option C is the right answer.