Quantitative Aptitude Question on Profit & Loss

Question

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

Answer 1

Solution

The correct answer is (B):
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
3a+2b/5 = 40/1.1
3.3a + 2.2b = 200--------(1)
The profit is 5% if the 2 varieties are mixed in the ratio 2:3.
2a+3b/5 = 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
a/b = 0.95/1.2
a/b = 19/24