Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R?

p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding ‘p’ both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding ‘q’ both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 – (p + q) => r = Rs.500.