Pure Ghee costs Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50 per kg. A shopkeeper sells the mixture at Rs.96 per kg. Thereby making a profit of 20%. In what ratio does he mix the two?

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1:2

3:2

3:1

2:3

answer is B.

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Detailed Solution

Let us assume that the cost of pure ghee and vegetable oil together as x.

Now, the cost of mixture can be written as the sum of the cost of them together and the profit.
⇒cost of mixture

= x + 20

percrent of x
Given, in the question that the cost of the mixture is Rs.96

According to the percentage formula x% of y can be written as

\frac{x}{100} \times y

Now, we can write the equation as follows.

\Rightarrow x + \frac{20}{100} \times x = 96

This can be further simplified as.

\Rightarrow \frac{100 x + 20 x}{100} = 96

Now, this can also be written as.

\Rightarrow \frac{120 x}{100} = 96

Let us now multiply with 100 on both the sides.

\Rightarrow 120 x = 96 \times 100

Now, on dividing with 120 on both the sides we get,

\Rightarrow x = \frac{9600}{120} ∴ x = Rs . 80

Now, this is the original cost of the pure ghee and vegetable oil together.

Given, that

Cost of pure ghee per kg is Rs.100

Cost of vegetable oil per kg is Rs.50

As we already know that Rs.80 is the original cost of the mixture per kg so if we consider the amount of ghee as y then the amount of vegetable oil will be the remaining in the 1 kg mixture.

Now, we can write this as: