A vessel contains 208 liters’ mixture of milk and water mixed in the ratio 11 ∶ 5. ‘8x’ liters of mixture are taken out of the vessel and replaced with ‘3x – 4’ liters of water so that the ratio of milk to water in the vessel becomes 4 : 3 respectively. Find the difference between the final quantities of milk and water in the vessel.
A. 21 liters
B. 22 liters
C. 23 liters
D. 24 liters
Answer: 22 liters
Sol:
A vessel contains 208 liters’ mixture of milk and water mixed in the ratio 11 ∶ 5
Initial quantity of milk in the vessel = 208 × (11/16) = 143 liters
Initial quantity of water in the vessel = 208 × (5/16) = 65 liters
So, ‘8x’ liters mixtures contain 5.5x liters milk and 2.5x liters water
According to the question,
⇒ (143 – 5.5x)/(65 – 2.5x + 3x – 4) = 4/3
⇒ 429 – 16.5x = 244 + 2x ⇒ 18.5x = 185
⇒ x = 10
So, the final quantity of milk = 143 – 55 = 88 liters
Final quantity of water = 65 – 25 + 30 – 4 = 66 liters
The difference between the final quantities of milk and water in the vessel = 88 – 66 = 22 liters
∴ The required value is 22 liters.
