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:
Solution
Correct Answer: Option C
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.
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions