Question

A seven-litre vessel contains a mixture of milk and water. Milk is 49% of the total volume. A few litres of the mixture is taken out and replaced by an equal amount of water. This process is repeated twice and now the milk is 9% only. How many litres of the mixture is taken out each time?

Answer 1

Answer:

Let the vessel contains 8 litres of liquid.

Let x litres of this liquid be replaced with water

when x litre of mixture is taken out it means

8

5x

litre milk and

8

3x

litre water taken out

Quantity of water in new mixture =(3−

8

3x

+x)litres

Quantity of milk in new mixture =(5−

8

5x

)litres

∴(3−

8

3x

+x)=(5−

8

5x

)

⇒5x+24=40−5x

⇒10x=16

∴x=

5

8

So, part of the mixture replaced =(

5

8

×

8

1

)=

5

1

.