Arithmetic

Mixture & Alligation

Medium

applied

A container contains 100 liters of milk. From this container, 10 liters of milk is taken out and replaced by water. This process is repeated two more times.The amount of milk left in the container now is:

85 liters

70 liters

67.1 liters

72.9 liters

✅ Correct Option: 4

The container initially contains 100 liters of pure milk.

After the first replacement:

10 liters of milk is removed, leaving 90 liters of milk.

10 liters of water is added to fill the container back to 100 liters.

The container now has 90 liters of milk and 10 liters of water.

After the second replacement:

The container has 90% milk and 10% water.

When 10 liters of mixture is removed, the milk removed is:

$10 \times \dfrac{90}{100} = 9$ liters

Milk remaining:

$90 - 9 = 81$ liters

10 liters of water is added to fill the container back to 100 liters.

The container now has 81 liters of milk and 19 liters of water.

After the third replacement:

The container has 81% milk and 19% water.

When 10 liters of mixture is removed, the milk removed is:

$10 \times \dfrac{81}{100} = 8.1$ liters

Milk remaining:

$81 - 8.1 = 72.9$ liters

Alternatively, using the formula:

Milk remaining $= \text{Initial amount} \times \left(1 - \dfrac{\text{amount removed}}{\text{total volume}}\right)^{\text{number of replacements}}$

$= 100 \times \left(1 - \dfrac{10}{100}\right)^3$

$= 100 \times (0.9)^3$

$= 100 \times 0.729$

$= 72.9$ liters

Therefore, the amount of milk left in the container is 72.9 liters.

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A container contains 100 liters of milk. From this container, 10 liters of milk is taken out and replaced by water. This process is repeated two more times.The amount of milk left in the container now is:

Solution

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