Question

5. 8 Liters are drawn off from a can filled with milk and it is then filled with water. This operation is

performed three more times. The ratio of the quantity of milk now left in the can to that of the total

mixture is 16:81. How much milk did the can hold originally?

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Answer 1

Step-by-step explanation:

This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally? The correct option is D.

Answer 2

Given:

8 Liters are drawn off from a can filled with milk and it is then filled with water. This operation is  performed three more times. The ratio of the quantity of milk now left in the can to that of the total  mixture is 16:81.

To Find:

How much milk did the can hold originally?

Solution:

It is given that 8 litres are withdrawn from a can filled with milk and then replaced by water and it is further performed three more times and the ratio of the quantity of milk now left in the can to that of the total  the mixture is 16:81 and then we need to find the milk initially in the can,

If a vessel contains 'a' litres pf liquid A and 'b' litres is withdrawn and replaced by liquid B, then

$\frac{Liquid A left}{Initial A} =[\frac{a-b}{a}]^n$

So by using this formula we can say that

$\frac{16}{81} =[\frac{a-8}{a}]^4 \\\frac{2}{3} =\frac{a-8}{a} \\a=24L$

Hence, 24L of milk the can originally hold.