RAS question
A starts a business with ₹45,000. After 4 months, B joins with ₹60,000. At the end of the year, the profit is ₹85,000. What is B's share of the profit?
Correct answer: (D) ₹40,000.
B's share of the annual profit is Rs 40,000 because, when partners invest for unequal periods, profit is divided in the ratio of capital multiplied by time.
Explanation
This is a compound partnership question because A and B invested for different periods. SATHEE's partnership rule says that profit or loss is shared in the ratio of investment, calculated as capital multiplied by time. A invests Rs 45,000 for the full 12 months, so A's capital-time product is 45,000 × 12 = 5,40,000. B joins after 4 months and therefore invests Rs 60,000 for 8 months, so B's capital-time product is 60,000 × 8 = 4,80,000. The ratio is 5,40,000 : 4,80,000, which reduces to 9 : 8. Out of the total profit of Rs 85,000, B gets 8 of the 17 parts: (8/17) × 85,000 = Rs 40,000.
Why the other options are wrong
- (A) Choosing Rs 35,000 amounts to assigning B 7 of the 17 parts, but the 9 : 8 capital-time ratio gives B 8 parts.
- (B) Rs 45,000 may look plausible because it is close to B's capital, but it is larger than B's 8/17 share; profit is divided by capital multiplied by time rather than capital alone.
- (C) Rs 48,000 may be confused with B's capital-time product of 4,80,000, but that product is used to form the ratio and is not B's final profit share.
Concept
In Reasoning and Mental Ability, this is a compound partnership problem under ratio and proportion. When partners invest for unequal periods, profit is divided in the ratio of capital multiplied by time. RAS repeatedly uses this pattern because it tests arithmetic accuracy and whether the candidate notices that a partner joined late.