Question

3 years ago A was 4 times as old as B. After 18 years A age will exceed B’s age by 12 years. The ratio of present ages of A and B is?

Answer 1

three year ago the age of A is x-3
B is 4 (y-3)
here
(x-3)=4 (y-3)
by solve mark as equation 1
x+18= x+18 multiply y-12 mark as equation 2
solving both find x and y you get the present age

Answer 2

3 years ago A was 4 times as old as B
so, A = 4B then ratio be A:B = 4:1............(1)
After 18 years A's age will exceed B's age by 12 years so, let B's age be x
A = B + 12 or A = x + 12
now ratio be A:B =(x + 12): x
now reduce 21(18+3) years from above ratio
reduced ratio will be
A:B = (x + 12 - 21):(x-21)..............(2)
equate ratio(1) = ratio(2)
4/1 = (x-9)/(x-21)
4x - 84 = x - 9
3x = 75
x = 25
B's age = x = 25
then A's age = x + 12 = 25 + 12 = 37