A printing press is run by Neha and Arjun. Neha supplies \(\frac{4}{9}\) of the capital, and her money is used for 15 months. Arjun supplies the remaining capital. If the profit is shared equally between them, for how many months was Arjun’s money used?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 12 months
The profit is shared in the ratio of capital \(\times\) time. An equal share means the two products are equal.
Arjun’s part of the capital \(\displaystyle =1-\frac{4}{9}=\frac{5}{9}\)
Let Arjun’s money be used for \(t\) months. Then \(\displaystyle \frac{4}{9}\times15=\frac{5}{9}\times t\)
Multiplying by 9: \(60=5t\)
\(t=12\)
Arjun’s money was used for 12 months.
Why the other options are incorrect
Option (1) 9 months — Incorrect. The ratio would be \(60:45=4:3\), so Neha would get more than Arjun.
Option (2) 10 months — Incorrect. The ratio would be \(60:50=6:5\), so the shares would still not be equal.
Option (4) 15 months — Incorrect. Arjun has the larger capital, so the same 15 months would give him more: \(60:75=4:5\).