Farah opened a tailoring shop with Rs 45,000. Later in the year Gopal became her partner and brought in Rs 60,000. When the profit of the year was shared, Farah got Rs 3 for every Rs 2 that Gopal got. How many months after the shop opened did Gopal join?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 months
The profit is shared in the ratio of capital \(\times\) number of months the money was in the shop.
Farah’s money was in for all 12 months: \(45000\times12=540000\)
Let Gopal’s money be in for \(t\) months: \(60000\times t\)
Farah : Gopal \(=3:2\), so \(540000\times2=60000t\times3\)
\(1080000=180000t\), so \(t=6\)
Gopal’s money was in for the last 6 months, so he joined \(12-6=6\) months after the opening
Gopal joined 6 months after the shop opened.
Why the other options are incorrect
Option (1) 4 months — Incorrect. Gopal’s money would be in for 8 months: \(540000:480000=9:8\), not \(3:2\).
Option (2) 5 months — Incorrect. Gopal’s money would be in for 7 months: \(540000:420000=9:7\).
Option (4) 8 months — Incorrect. Gopal’s money would be in for only 4 months: \(540000:240000=9:4\).