The ratio of the age of P and Q is 7 : 4 . After 6 years their age will be in the ratio of 5 : 3 . Find the ratio of the sum and difference of the present ages of P & Q.

33 : 9

Let age of P   = 7x and age of Q  = 4x 

Now , according to question 

\(\frac{7x+ 6}{4x+6}\) = \(\frac{5}{3}\)

21x  + 18 = 20x + 30

x = 12

so,       

Sum of present age of  Present age of P & Q =  ( 12 x 7 ) + ( 12 x 4 )  = 132

Difference of  present age of  Present age of P & Q  = 84 - 48  = 36

Required ratio    ( P + Q )   :   (P - Q ) 

                           132       :    36

                            33       :     9