An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q?

Questions: An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q?

Solution:
Let the amount to be distributed be Tk x.
P : Q : R = 2 : 7 : 9
Sum of the ratios = 2 + 7 + 9 = 18

P = (2/18) × x = x/9
Q = 7x/18
R = 9x/18 = x/2

As given, (x/9) + (7x/18) = (x/2)
⇒ (2x + 3x)/18 = (x/2)
⇒ x/2 = x/2
Thus, we get no conclusion. Amount should necessarily be known.