Question

A vessel of 160 L is filled with milk and water.70% of milk and 30% of water is taken out of the vessel.It is found out that the vessel is vacated by 55%,then the quantity of milk and water in the original mixture is

• A. Milk 100 L; Water = 60 L
• B. Milk 60 L; Water = 100 L
• C. Milk 90 L: Water = 70 L
• D. Milk 70 L; Water = 90 L

Answer 1

The Correct Option is A

Let the quantity of milk and water in the vessel initially be \( M \) and \( W \), respectively. We know:

\[ M + W = 160 \]

Out of the total milk, 70% is retained, and after removing 55% of the mixture:

\[ 0.3M + 0.7W = 0.45 \times 160 = 72 \]

Now, we have the system of equations:

\[ M + W = 160 \quad \text{(1)} \]

\[ 0.3M + 0.7W = 72 \quad \text{(2)} \]

Multiply equation (1) by 0.3:

\[ 0.3M + 0.3W = 48 \quad \text{(3)} \]

Subtract equation (3) from equation (2):

\[ (0.3M + 0.7W) - (0.3M + 0.3W) = 72 - 48 \]

\[ 0.4W = 24 \quad \Rightarrow \quad W = 60 \]

Substitute \( W = 60 \) into equation (1):

\[ M + 60 = 160 \quad \Rightarrow \quad M = 100 \]

Thus, the quantity of milk is 100 L and the quantity of water is 60 L.