The ratio of ages of A and B, 9 years ago was 3 : 4 .  Four years ago, the ratio of their ages was 2 : 3.  What will be the ratio of their ages 5 years from now?

29 : 34

A    :    B

3    :    4   →  9 years ago

2    :    3   →  4 years ago

ATQ,

\(\frac{3x + 5}{4x + 5}\) = \(\frac{2}{3}\)

9x + 15 = 8x + 10

x = 5

Therefore,

  A     :      B

 3x    :     4x    (9 years ago)

 15    &     20   (as x = 5)

present age of A =15 + 9 = 24

After 5 years age of A = 24 + 5 = 29 years 

present age of B = 20 + 9 = 29 years 

After 5 years age of B = 29 + 5 = 34 years 

 required ratio      29     :      34    (after 5 years from now)