A, B, and C enter a partnership with shares proportional to 7/2 : 4/3 : 6/5. After 4 months, A increases his investment by 50%. If the total profit at the end of one year is Rs. 21600, what is B’s share?

Introduction / Context:
This involves unequal base shares and a mid-year change. Compute time-weighted contributions: for A there are two phases (first 4 months at base, next 8 months at 1.5 times base). B and C remain constant for the whole year.

Given Data / Assumptions:

• A = (7/2)k for 4 months; then 1.5 × (7/2)k for 8 months.
• B = (4/3)k for 12 months.
• C = (6/5)k for 12 months.
• Total profit = Rs. 21600; shares ∝ capital × time.

Concept / Approach:
Compute units for each partner, sum to get total units, then compute B’s fraction times the profit.

Step-by-Step Solution:
A units = (7/2)k*4 + (3/2)*(7/2)k*8 = 14k + 42k = 56kB units = (4/3)k*12 = 16kC units = (6/5)k*12 = 72/5 k = 14.4kTotal units = 56k + 16k + 14.4k = 86.4kB’s fraction = 16/86.4 = 160/864 = 5/27B’s share = 21600 * (5/27) = 800 * 5 = Rs. 4000

Verification / Alternative check:
The simplification 16/86.4 = 5/27 ensures exact arithmetic with 21600 divisible by 27.

Why Other Options Are Wrong:
Other amounts correspond to different fractions of the total and do not match the computed 5/27 share.

Common Pitfalls:
Forgetting A’s 50% increase or mis-splitting the 12 months into 4 + 8.

Final Answer:
Rs. 4000