A sum of Rs.1200 is shared among P, Q, and R. P receives half the combined amount of Q and R. Q obtains one-third of the total amount received by P and R. What is the share of R?

Explanation

Let the shares of P, Q, and R be p, q, and r respectively. Given, p + q + r = 1200. P gets half of (q + r), so p = 1/2 (q + r), which implies 2p = q + r. Adding p on both sides gives 3p = p + q + r = 1200, hence p = Rs.400. Q receives one-third of (p + r), so q = 1/3 (p + r), leading to 3q = p + r. Adding q on both sides results in 4q = p + q + r = 1200, so q = Rs.300. Therefore, R's share is r = 1200 - (p + q) = Rs.500.