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
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.