Question

A vessel contains 60 litres milk. 10 litre of the milk is taken out of the vessel and replaced with water. This procedure is repeated once more. Now 60 litre milk is poured into the vessel. And again 10 litre of mixture is taken out of the vessel and replaced with water. Find the ratio of milk and water in vessel finally.

Answer 1

Step-by-step explanation:

=> Initially the volume of milk = 60L

• After first condition

=> Ratio of milk to water = (60-10):10 = 5:1

So , milk in container is (5/6) part of vessel

• After second replacement

the mixture contains milk in ratio of 5:1 i.e. removal of 10L of mixture results in

{(5/6)×10= 8.3333L} of milk and { (1/6)×10 = 1.6667L} of water is removed and 10 L of water is added

Now, we can say the resultant quantity of milk = 50L - 8.333 L = 41.6667L

the resultant quantity of water = 10 L - 1.6667L + 10L =18.333L

• Now the 60L of milk is added so,

final volume of milk = 60+41.6667 = 101.6667 L

• Now again the last replacement takes place

The mixture now consists of = 101.6667 + 18.3333L =120 L

so from 10 L of mixture

=> Volume of milk = {101.6667/120}×10 = 8.472225 L

=> Volume of water = 10 - 8.472225 = 1.527775 L

now adding 10 L of water

Hence final Volume of milk in mixture

= 101.6667 - 8.472225 = 93.2 L

Final volume of water in mixture

= Total volume of mixture - Total volume of milk = 120 L -93.2L = 26.8L

Hence the ratio of the milk to water in mixture is

=> 93.2 : 26.8 = 7:2 approx