A, B, and C enter a partnership with capitals in the proportion 1/3 : 1/4 : 1/5. A withdraws half his capital after 4 months. Out of a total annual profit of Rs. 847, what is A’s share?

Introduction / Context:
This partnership involves unequal capitals (given as fractions) and a mid-year capital change. Profits must be divided using capital × time. Track A’s two phases (before and after withdrawal) separately.

Given Data / Assumptions:

• Capital ratio: 1/3 : 1/4 : 1/5.
• A halves his capital after 4 months.
• Total profit for 12 months = Rs. 847.

Concept / Approach:
First clear fractions to convenient integers. Take LCM(3,4,5)=60 to get equivalent capitals 20 : 15 : 12. Then compute time-weighted units: A at full for 4 months and at half for 8 months; B and C unchanged for 12 months.

Step-by-Step Solution:
Equivalent capitals: A = 20, B = 15, C = 12A units = 20*4 + (10)*8 = 80 + 80 = 160B units = 15*12 = 180C units = 12*12 = 144Total units = 160 + 180 + 144 = 484A’s share = 847 * (160/484) = 847 * (40/121) = (847/121)*40 = 7*40 = Rs. 280

Verification / Alternative check:
Because 121*7 = 847, the fraction simplifies neatly, confirming the computed share.

Why Other Options Are Wrong:
Rs. 252, Rs. 315, and Rs. 412 result from incorrect unit counts or forgetting that A halved his capital.

Common Pitfalls:
Using only the initial ratio for the whole year; ignoring the halving event leads to an over-allocation to A.

Final Answer:
Rs. 280