From a container of wine a man stolen 15… | Answer | TuitionWave

Subject

Quantitative Aptitude

Topic

Miscellaneous

From a container of wine a man stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus in three attempts the ratio of water and wine becomes 169 : 343. The initial amount of wine in the container was:
Reading

ক)

130 litres

খ)

140 litres

গ)

120 litres

ঘ)

90 litres

ঙ)

None of these

Explanation

Let the initial amount of wine in the container was k, then according to the question,

\frac{{wine\ left}}{{water\ added}} = \frac{{343}}{{169}}

It means –

\frac{{wine\ left}}{{water\left( {initial\ amount} \right)}} = \frac{{343}}{{512}}

(because 343 + 169 = 512) Thus,

\begin{array}{l} 343x = 512x{\left( {1 - \frac{{15}}{k}} \right)^3}\\ \Rightarrow \frac{{343}}{{512}} = {\left( {\frac{7}{8}} \right)^3} = {\left( {1 - \frac{{15}}{k}} \right)^3}\\ \Rightarrow \left( {1 - \frac{{15}}{k}} \right) = \frac{7}{8} = \left( {1 - \frac{1}{8}} \right) \end{array}

∴ k = 120 Hence, the initial amount of wine in the container was 120 litres.

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