48 litre of Glycerin is mixed with 144 litre Rose water. D litre of total mixture is taken out and 32 litre Glycerin and 48 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.Choices:- 24 32 40 20
Question
48 litre of Glycerin is mixed with 144 litre Rose water. D litre of total mixture is taken out and 32 litre Glycerin and 48 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.Choices:- 24 32 40 20
Solution
The initial quantity of Glycerin is 48 litres and Rose water is 144 litres. So, the total quantity of the mixture is 48 + 144 = 192 litres.
Let's assume that D litres of the mixture is taken out. So, the quantity of the mixture left is 192 - D litres.
In this remaining mixture, 32 litres of Glycerin and 48 litres of Rose water are added. So, the total quantity of the mixture now becomes 192 - D + 32 + 48 = 272 - D litres.
According to the problem, the final mixture contains 30% Glycerin. So, the quantity of Glycerin in the final mixture is 30/100 * (272 - D) = 81.6 - 0.3D litres.
But we know that the initial quantity of Glycerin was 48 litres, out of which D litres were taken out and 32 litres were added. So, the final quantity of Glycerin should be 48 - D/4 + 32 = 80 - D/4 litres. (Since the ratio of Glycerin to Rose water in the mixture is 1:3, only 1/4th of the quantity taken out will be Glycerin)
Equating the two expressions for the quantity of Glycerin, we get:
81.6 - 0.3D = 80 - D/4 Solving this equation for D, we get D = 32 litres.
So, the quantity of the mixture that is taken out is 32 litres. Therefore, the correct choice is 32.
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