Q. 2. There was 120 litres of pure milk in a vessel. Some quantity of milk was taken out replaced with 23 liters of water in such a way that the resultant ratio of the quantity of milk to that of water in the mixture was 4:1. Again 23 litres of the mixture was taken out and replaced with 28 litres of water. What is the ratio of milk to water in the resultant mixture?
Answers
Solution ;-
Let us assume that, x quantity of milk was taken out and replaced with 23 litre of water.
so, given that,
→ Milk : water = 4 : 1
→ (120 - x) : 23 = 4 : 1
→ (120 - x) / 23 = 4/1
→ 120 - x = 23 * 4
→ 120 - x = 92
→ x = 120 - 92
→ x = 28 litre.
Now, in the Mixture we have :-
- Milk = 120 - 28 = 92 litre .
- water = 23 litre .
given that, again 23 litre of mixture was taken out and replaced with 28 litre of water .
then,
→ Quantity of milk was taken out in 23 litre of mixture = (4/5) * 23 = 18.4 litre .
and,
→ Quantity of water was taken out in 23 litre of mixture = (1/5) * 23 = 4.6 litre .
therefore,
→ Milk left in mixture now = 92 - 18.4 = 73.6 litre .
and,
→ Water left in mixture now = 23 - 4.6 = 18.4 litre .
now, we have given that, 28 litres of was added.
hence,
→ Milk = 73.6 litre .
→ water = 18.4 + 28 = 46.4 litre .
∴
→ Required ratio = M : W = 73.6 : 46.4 = 184 : 116 = 46 : 29 (Ans.)
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