A sum of Rs. 3600 is distributed among A, B and C. A gets 1/3 of what B and C…

Concept: If a person's share X equals (m/n) of the sum of the other two shares, then since the sum of the other two shares equals Total minus X, we get: n·X = m·(Total − X), which simplifies to X = m·Total / (m+n). This is the standard shortcut for a three-way distribution where one share is given as a fraction of the sum of the other two.

Application:

1. Let the total sum be T = Rs 3600, with A, B, C denoting the shares of A, B and C respectively, so A + B + C = 3600.

2. A gets 1/3 of what B and C got together: A = (1/3)(B + C). Since B + C = 3600 − A, this gives 3A = 3600 − A, so 4A = 3600, i.e. A = Rs 900.

3. C gets 1/2 of what A and B got together: C = (1/2)(A + B). Since A + B = 3600 − C, this gives 2C = 3600 − C, so 3C = 3600, i.e. C = Rs 1200.

Cross-check: B = 3600 − 900 − 1200 = Rs 1500. Check A's condition: B + C = 1500 + 1200 = 2700, and (1/3)(2700) = 900 = A. Check C's condition: A + B = 900 + 1500 = 2400, and (1/2)(2400) = 1200 = C. Total = 900 + 1500 + 1200 = 3600, which matches the given sum. So C's share = Rs 1200.