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 the profit ratio is based on 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, taken as capital multiplied by time. A invests Rs 45,000 for the full 12 months, so A's investment-time is 45,000 x 12 = 5,40,000. B joins after 4 months, so B invests Rs 60,000 for 8 months: 60,000 x 8 = 4,80,000. The ratio is therefore 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) x 85,000 = Rs 40,000.
Why the other options are wrong
- (A) Rs 35,000 would understate B's share; the reduced capital-time ratio gives B 8 out of 17 parts, not 7 out of 17.
- (B) Rs 45,000 treats B's share as larger than the 8/17 share produced by the 9:8 investment-time ratio.
- (C) Rs 48,000 is B's investment-time figure after dropping two zeroes, not B's share of the Rs 85,000 profit.
Concept
This tests compound partnership under ratio and proportion: profit is divided by capital multiplied by time when partners invest for unequal periods. RAS repeatedly uses this pattern because it checks arithmetic accuracy and whether the candidate notices the delayed entry of a partner.