UPSC Prelims 2002 Q104: Science & Technology – Quantitative Aptitude
Amit started a business by investing Rs 30,000. Rahul joined the business after some time
and invested Rs 20,000. At the end of the year, profit was divided in the ratio of 2 :
1. After how many months did Rahul join the business?
- (a) 2
- (b) 3
- (c) 4
- (d) 5
Answer: (b) 3
Explanation
Month in which Rahul joined Amit's business
| Partner | Investment x time |
|---|---|
| Amit | Rs 30,000 for 12 months = 3,60,000 |
| Rahul | Rs 20,000 for (12 − x) months = 20,000 (12 − x) |
| Profit ratio | Amit : Rahul = 2 : 1 |
| Equation | 3,60,000 = 2 × 20,000 (12 − x), so 12 − x = 9 and x = 3 |
Profit is shared in the ratio of investment multiplied by time. Amit's share is 30,000 × 12 = 3,60,000, and for a 2 : 1 ratio Rahul's share must be 1,80,000, which is 20,000 for 9 months. So Rahul joined after 3 months.
Answer: (b) 3.
Why each option is right or wrong
- (a) Incorrect. Joining after 2 months gives Rahul 10 months and a ratio of 1.8 : 1.
- (b) CORRECT. Rahul invested for 9 months, giving 3,60,000 : 1,80,000 = 2 : 1.
- (c) Incorrect. Joining after 4 months gives Rahul 8 months and a ratio of 2.25 : 1.
- (d) Incorrect. Joining after 5 months gives Rahul 7 months and a ratio of about 2.6 : 1.
Key point
In partnership problems the profit ratio equals the ratio of (capital × months).
Remember
Profit ratio = capital × time ratio.
Common mistakes
- Using only the capital ratio 3 : 2 and ignoring time.
- Counting the 9 months Rahul worked as the answer.
- Forgetting that the year has 12 months.
Exam tip
Rahul's 9 months = 12 − 3; test option (b) first.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Partnership)