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 ?->(Show Answer!)

1. 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

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By: anil on 05 May 2019 02.28 am

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,
$$3.3a+2.2b = 2.1a+3.15b$$
$$1.2a=0.95b$$
$$frac{a}{b} = frac{0.95}{1.2}$$
$$frac{a}{b} = frac{19}{24}$$

Therefore, option C is the right answer.

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