Question

the ages of A and B are in the ratio of 5:3 after 6 years their ages will be in the ratio of 7:5 .the sum of their present ages is ?

Answer 1

Let present ages of A and B be 5x and 3x respectively

After six years,

Age of A: 5x +6

Age of B: 3x+ 6

According to question

(5x+6)/(3x+6) = 7/5

5(5x+6)  = 7(3x+6)

25x + 30 = 21x + 42

25x - 21x = 42 -30

4x = 12

x = 3

So, age of A = 5x = 15

And, age of B = 3x = 9

So answer is sum of their ages that is 15+9 which is 24

Answer 2

Let their present ages be 5x and 3x

After 6 years,

5( 5x + 6)     =    7(3x +6)

25x  +  30    =    21x  +  42

25x   -   21x  =    42  -   30

          4x      =     12

                x   =   3

Hence present age of A = 5x  =   5*3   =   15 years

                           and   B = 3x  =  3*3     =   9 years