Three friends (Amar, Mohan and Sham) started partnership business by investing…
2024
Three friends (Amar, Mohan and Sham) started partnership business by investing Rs. 1,00,000, Rs. 1,40,000 and Rs. 1,60,000 respectively. After eight months, Ramesh joins them with his capital of Rs. 50,000. If, at the end of the year, a profit of Rs. 30,500 was made, what would be the difference between the shares of Sham and Mohan?
- A.
Rs. 675
- B.
Rs. 950
- C.
Rs. 1200
- D.
Rs. 1464
Attempted by 5 students.
Show answer & explanation
Correct answer: D
Concept: When partners invest for different lengths of time, profit is shared in the ratio of investment multiplied by time period (capital multiplied by the number of months invested), not in the ratio of capital alone. This is because profit accrues in proportion to how much capital was at work and for how long.
Amar invests Rs. 1,00,000 for the full 12 months: 1,00,000 × 12 = 12,00,000.
Mohan invests Rs. 1,40,000 for the full 12 months: 1,40,000 × 12 = 16,80,000.
Sham invests Rs. 1,60,000 for the full 12 months: 1,60,000 × 12 = 19,20,000.
Ramesh joins after eight months, so he invests Rs. 50,000 for the remaining 12 − 8 = 4 months: 50,000 × 4 = 2,00,000.
Dividing each value by the common factor 40,000, the ratio Amar : Mohan : Sham : Ramesh = 30 : 42 : 48 : 5, with total parts = 30 + 42 + 48 + 5 = 125.
Sham's share = (48/125) × 30,500 = Rs. 11,712.
Mohan's share = (42/125) × 30,500 = Rs. 10,248.
Difference between Sham's and Mohan's shares = 11,712 − 10,248 = Rs. 1,464.
Cross-check: The four shares should add up to the total profit — Amar's share (30/125 × 30,500 = Rs. 7,320) + Mohan's (Rs. 10,248) + Sham's (Rs. 11,712) + Ramesh's (5/125 × 30,500 = Rs. 1,220) = Rs. 30,500, which matches the total profit, confirming the ratio and shares are correct.