There are five friends, P, Q, R, S and T. P says to Q, “If you give me Rs 300, you will have as many as I have at this moment. If S takes Rs 500 from you, he will have as much money as T has now. P and R together has twice much money as T has. Q and S combined have same amount of money as P and R combined. If together they have Rs 15000, How much money R has?

Solution

P takes 300 from Q i.e., P + 300 = Q – 300 Q – P = 600 ---------------------------(1) S takes 500 from Q, then Q – 300 – 500 = T Q – 800 = T ----------------------------(2) P + R = 2T ---------------------------- (3) Q + S = P + R -------------------------(4) Put equation (3) in (4), we get Q + S = 2T -----------------------------(5) Total, P + Q + R + S + T = 15000 Put (3) & (5) 2T + 2T + T = 15000 5T = 15000 T = 3000 Put T in (2) Q = 3800 Put Q in (1) P = 3200 Put P and T in (3) 3200 + R = 6000 R = 2800