Question

the age of A and B are in the ratio 8:3 six years hence their ages will be in the ratio 9:4 find their present ages

Answer 1

Let the coefficient be x.
A's age = 8x
B's age = 3x
Six years hence,
Ages will be 8x+6 and 3x+6.
Now, As per the question,
(8x+6) /(3x+6) = 9/4
32x+24 = 27x+54
5x = 30
x = 6.
Present ages of A and B will be 48 and 18 years.

Answer 2

...let their age now is 8x,3x yrs
after six yrs their age will be 8x+6,3x+6 yrs
so 8x+6=9y... (1)
and 3x+6 =4y...... (2)
solving them
we get x=6,y=6....
so their present age is 48,18 yrs respectively