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A vessel contains a mixture of milk and water in the respective ratio of 3 : 1. 32 litre of mixture was taken out and replaced with the same quantity of milk so that the resultant ratio between the quantities of milk and water in the mixture was 4 . : 1 respectively. If 10 litre of mixture is again taken out from the vessel, what is the resultant quantity of water in the mixture ? (in litre)
A) 24
B) 30
C) 20
D) 36
E) 32
Correct answer:
B) 30
Description for Correct answer:
Let the total quantity of mixture = x litre
According to question,
\( \frac{4}{4+1}=\left[ \frac{x-32}{x} \right] \)
4x=5x-160
x = 160 Litrs
The quantity of milk in mixture = \( 160 \times \frac{3}{4} \)
= 120 Litre
The quantity of water in misture = \( 160 \times \frac{1}{4} \)
= 40 Litre
32 litre of mixture was taken out and replaced with the same quantity of milk.
Then, the quantity of milk in mixture = \( 120-32 \times \frac{3}{4}+32 \)
= 120-24+32 = 128 Litre
After 10 litres of mixture is again taken out from the vessel, the resultant quantity of water
in the mixture = \( 32-10 \times \frac{1}{5} = 32 - 2 = 30 litre \)
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