8 litres are drawn from a cask filled with wi… | GMAT Sprint

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PS · Problem Solving

705-805

Fractions/Ratios/Decimals

8 litres are drawn from a cask filled with wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the total solution is $16:81$ . How much wine did the cask hold originally?

Answer Choices

Correct answer marked below

24 litres

Correct

44 litres

45 litres

49 litres

50 litres

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Explanation

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Official Explanation

Official

Let the original quantity of wine in the cask be

x

litres.

When 8 litres are drawn from the cask and replaced with water, the fraction of wine remaining is

1 - \frac{8}{x}

.

This operation is performed a total of four times, so the wine left after four replacements is:

x \left(1 - \frac{8}{x}\right)^4

Given the ratio of wine left to total solution is

16:81

, we have:

\frac{x \left(1 - \frac{8}{x}\right)^4}{x} = \frac{16}{81}

…

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What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.

8 litres are drawn from a cask filled with wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the total solution is 16:8116:8116:81. How much wine did the cask hold originally?