A, B and C invest in the ratio 7⁄2 : 4⁄3 : 6⁄5. After 4 months, A increases his investment by 50%. If the total profit after one year is Rs. 21,600, what is B's share?

Problem restatement
Profits are proportional to (capital × time). A invests in two phases: first 4 months at his original capital; next 8 months at 1.5 times that capital. B and C keep their capitals constant for 12 months.

Given data

• Capital ratios: A : B : C = 7⁄2 : 4⁄3 : 6⁄5
• Time: total 12 months; A increases capital after 4 months by 50%
• Total profit = Rs. 21,600

Concept/Approach
Convert fractional ratios to a common integer base and compute time-weighted contributions.

Step-by-step calculation
Choose base so that A = 105, B = 40, C = 36 (LCM of denominators 2,3,5 → 30; so 7⁄2=105⁄30, 4⁄3=40⁄30, 6⁄5=36⁄30)A's contribution = 4×A + 8×(1.5A) = 4A + 12A = 16A = 16×105 = 1680B's contribution = 12×B = 12×40 = 480C's contribution = 12×C = 12×36 = 432Total = 1680 + 480 + 432 = 2592B's profit share fraction = 480 ÷ 2592 = 5 ÷ 27B's profit = 21,600 × (5÷27) = Rs. 4,000

Verification/Alternative
Fraction 5⁄27 ≈ 0.185185; 0.185185 × 21,600 = 4,000.

Common pitfalls
Multiplying A's capital by 1.5 for the full 12 months (the increase starts after 4 months only).

Final Answer
Rs. 4,000