Vessels A and B contain 60 litres of alcohol and 60 litres of water, respectively. A certain volume is taken out from A and poured into B. After stirring, the same volume is taken out from B and poured into A. If the resultant ratio of alcohol and water in A is $15 : 4$, then the volume, in litres, initially taken out from A is:
Type your answer below:
âš¡ AZUCATION SHORTCUT:
After the two-way exchange of volume $x$, the volume in A returns to 60L.
Final Alcohol in A = $\frac{15}{19} \times 60$.
Using the exchange relation: $\frac{60^2}{60+x} = \frac{15 \times 60}{19}$
$\implies \frac{60}{60+x} = \frac{15}{19} \implies \frac{4}{60+x} = \frac{1}{19} \implies 60+x = 76 \implies \mathbf{x = 16}$.
Detailed Step-by-Step Solution
1. First Transfer: $x$ L alcohol moves A → B. Vessel B total volume becomes $60+x$ L.
2. Second Transfer: $x$ L mixture moves B → A. The alcohol concentration in B was $\frac{x}{60+x}$.
Alcohol moved back to A $= x \times \left( \frac{x}{60+x} \right) = \frac{x^2}{60+x}$.
Azucation established in 2013 is a leading CAT coaching institute in Ranchi, Jharkhand with a vision to impart empirical learning in competitive exams in a classroom coaching.
