Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of the water is 16 : 65. How much wine did the cask hold originally?
(a)18 litres
(b)24 litres
(c)32 litres
(d)42 litres
Answer
Answer (as printed): B
Explanation
Let the original quantity of the wine be $x$ litres. Then, $y=8, n=4$. Quantity of wine in the final mixture $=\left[x\left(1-\frac{8}{x}\right)^{4}\right]$ litres $=\frac{x(x-8)^{4}}{x^{4}}$ litres. Quantity of water in the final mixture $=\left[x-\frac{x(x-8)^{4}}{x^{4}}\right]$ litres $=\left[\frac{x^{5}-x(x-8)^{4}}{x^{4}}\right]$ litres. $\therefore \frac{x(x-8)^{4}}{x^{5}-x(x-8)^{4}}=\frac{16}{65} \Rightarrow 65 x(x-8)^{4}$ $=16 x^{5}-16 x(x-8)^{4}$ $\Rightarrow 81 x(x-8)^{4}=16 x^{5}$ $\Rightarrow(x-8)^{4}=\frac{16}{81} x^{4}=\left(\frac{2}{3} x\right)^{4} \Rightarrow x-8=\frac{2}{3} x \Rightarrow \frac{x}{3}=8$ $\Rightarrow x=24$.
Explanation as extracted from the printed page; notation may be imperfect.