Anil and Sunil start a bakery. Anil puts in \(\frac{2}{5}\) of the total money, and the money stays in the bakery for 9 months. Sunil puts in the rest of the money, and at the end takes \(\frac{1}{2}\) of the profit. For how many months was Sunil’s money in the bakery?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6 months
Profit is shared in the ratio of capital × time; the profit shares give that ratio, and the capitals are known.
Sunil’s capital \(=1-\frac{2}{5}=\frac{3}{5}\) of the money; Anil takes \(1-\frac{1}{2}=\frac{1}{2}\) of the profit
\(\frac{2}{5}\times9:\frac{3}{5}\times t=\frac{1}{2}:\frac{1}{2}\)
\(\frac{3}{10} t=\frac{9}{5}\), so \(t=6\)
Sunil’s money was in the bakery for 6 months.
Why the other options are incorrect
Option (2) 10 months — Incorrect. With 10 months, Anil : Sunil \(=\frac{2}{5}\times9:\frac{3}{5}\times10=3:5\), so Sunil would take \(\frac{5}{8}\) of the profit.
Option (3) 4 months — Incorrect. With 4 months, Anil : Sunil \(=\frac{2}{5}\times9:\frac{3}{5}\times4=3:2\), so Sunil would take \(\frac{2}{5}\) of the profit.
Option (4) 9 months — Incorrect. With 9 months, Anil : Sunil \(=\frac{2}{5}\times9:\frac{3}{5}\times9=2:3\), so Sunil would take \(\frac{3}{5}\) of the profit.