A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

The tub initially contains 60 litres of milk. The process of removing 6 litres and replacing it with water is repeated 3 times.

Initially:

Milk = 60 litres

Water = 0 litres

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After the first operation:

6 litres of milk is removed.

Milk remaining = 60 - 6 = 54 litres

6 litres of water is added back.

Milk concentration = $\dfrac{54}{60} = 0.9$

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After the second operation:

6 litres of the mixture is removed. This mixture contains milk and water in the ratio present in the tub.

Milk removed = $6 \times \dfrac{54}{60}$

Milk removed = $6 \times 0.9 = 5.4$ litres

Milk remaining = $54 - 5.4 = 48.6$ litres

6 litres of water is added back.

Milk concentration = $\dfrac{48.6}{60} = 0.81$

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After the third operation:

6 litres of the mixture is removed.

Milk removed = $6 \times \dfrac{48.6}{60}$

Milk removed = $6 \times 0.81 = 4.86$ litres

Milk remaining = $48.6 - 4.86 = 43.74$ litres

6 litres of water is added back.

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Alternatively, using the formula for repeated dilution:

Final milk = Initial milk $\times \left(1 - \dfrac{\text{Removed}}{\text{Total}}\right)^{\text{Number of times}}$

Final milk = $60 \times \left(1 - \dfrac{6}{60}\right)^3$

Final milk = $60 \times \left(\dfrac{54}{60}\right)^3$

Final milk = $60 \times (0.9)^3$

Final milk = $60 \times 0.729$

Final milk = $43.74$ litres

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Therefore, the amount of milk remaining in the tub is 43.74 litres.