Question 23

# From a jar of wine containing 32 litres, 4 litres is drawn out, and the jar is filled up with water. If the same proportion of wine is further drawn out two more times, what proportion of wine to water will be there in the resulting mixture?

Solution

From 32 litres, 4 litres is drawn out and is replaced with water.

Proportion of wine drawn = 4/32 = 1/8th of the total volume of the wine in the mixture.

When wine is drawn out for the second time, $$(1/8)\times (28) = 3.5$$ litres of wine will be drawn out.

Wine remaining in the jar = 28-3.5 = 24.5 litres

When wine is drawn out for the third time, $$(1/8)\times (24.5) =3.0625$$ litres of wine will be drawn out.

Wine remaining in the jar = 24.5 - 3.0625 = 21.4375 litres

Water in the jar = 10.5625 litres

Ratio of wine remaining in the jar to water remaining in the jar = 343:169

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