Question

From a flask containing water, 9 litres is taken out. It is replaced with an equal quantity of pure milk. This process is performed twice. The ratio of water to milk in the flask now is 16 : 9. What is the volume of the flask? (a) 45 litres (b) 65 litres (c) 50 litres (d) 75 litres

Answer 1

Let there be x litres in the cask.

After n operations,

Water left in vessel / Original quantity = (1 – 9/x)n

16/25 = (1 – 9/x)2

4/5 = 1 – 9/x

∴ x = 45 litres.

Answer 2

Answer:

The correct answer is option(c) 50liters

Step-by-step explanation:

Given,

From a flask containing water, 9liters of water were taken out and replaced with an equal quantity of milk twice

The ratio of water to milk in the flask after replacement = 16:9

To find,

The volume of the flask

Solution:

Let the volume of the flask be 'x'

Since the flask contains water, the initial volume of water in the flask = x liters

Since 9 liters of water is replaced from the flask with milk two times

The volume of water after replacement = x - 2×9 = x - 18

The volume of milk in the flask after replacement  = 18liters

Since the ratio of water to milk in the flask after the replacement is 16:9, we have,

Hence after replacement, the volume of water in the flask is 16y and the volume of milk in the flask is 9yliters

The total volume of the flask = 16y+9y = 25y

Since the volume of milk in the flask after the replacement is 18liters, we have

9y = 18

y = 2

Total volume of the flask = 25y = 50liters

The correct answer is option(c) 50liters

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