1200 is 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.

Answer 1

1200 = P+Q+R P=(1/2)Q +(1/2)R and Q= (P+R)/3 The Last one can be rewritten as P+R= 3Q

or P=3Q-R so 3Q-R =(1/2)Q+(1/2)R or (5/2)Q=3/2)R or R=(5/3)Q.

soooo 1200 = (3Q-(5/3Q) + Q +(5/3)Q or 4Q= 1200 or Q= 300

Then R= (5/3)300 =500 and P = 1200- 500 -300 = 400