Meera opened a shop with Rs 36,000. Later in the year Imran became a partner and brought in Rs 48,000. When the profit of the year was shared, Meera got Rs 9 for every Rs 8 that Imran got. How many months after the shop opened did Imran join?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4 months
Profit is shared in the ratio of capital × months. Find how many months Imran’s money was in the shop, then count back from 12.
Let Imran’s money stay for \(m\) months: \(36000\times12:48000 m=9:8\)
\(8\times36000\times12=9\times48000 m\), so \(m=8\)
Imran joined \(12-8=4\) months after the start
Imran joined 4 months after the shop opened.
Why the other options are incorrect
Option (1) 3 months — Incorrect. If Imran joined after 3 months, the ratio would be \(36000\times12:48000\times9=1 : 1\), not 9 : 8.
Option (2) 8 months — Incorrect. If Imran joined after 8 months, the ratio would be \(36000\times12:48000\times4=9 : 4\), not 9 : 8.
Option (3) 6 months — Incorrect. If Imran joined after 6 months, the ratio would be \(36000\times12:48000\times6=3 : 2\), not 9 : 8.