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From a container filled with milk, 9 litres of milk are drawn and replaced with water.Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is

Updated On: Jan 15, 2026
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Correct Answer: 45

Solution and Explanation

Milk and Water Container Capacity Calculation

Let the initial volume of the container be \( V \) litres. The process involves two cycles of removing 9 litres of the mixture and refilling with 9 litres of water.

After the First Cycle:

The amount of milk remaining is \( V - 9 \) litres. The proportion of milk left is \( \frac{V - 9}{V} \).

After adding 9 litres of water, the total volume remains \( V \) litres, with 9 litres of water present.

After the Second Cycle:

The milk from the previous stage is reduced by the same proportion. The milk remaining after the second cycle is calculated as:

Remaining milk = \( \frac{V - 9}{V} \times (V - 9) = \left( \frac{V - 9}{V} \right)^2 \times V \) litres

Given Proportion:

The final ratio of milk to water is stated as 16:9. This implies the proportion of milk in the final mixture is \( \frac{16}{16+9} = \frac{16}{25} \).

Therefore, the quantity of milk remaining is \( \frac{16}{25}V \).

Equation and Solution:

We equate the two expressions for the remaining milk:

\[ \left( \frac{V - 9}{V} \right)^2 \times V = \frac{16}{25}V \]

Dividing both sides by \( V \):

\[ \left( \frac{V - 9}{V} \right)^2 = \frac{16}{25} \]

Taking the square root of both sides:

\[ \frac{V - 9}{V} = \frac{4}{5} \]

Cross-multiplying to solve for \( V \):

\[ 5(V - 9) = 4V \]

\[ 5V - 45 = 4V \]

\[ V = 45 \]

Result:

The calculated capacity of the container is 45 litres.

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