At present, ratio of age of mother to her daughter is 5 : 3 .  After 30 years the ratio will be 4 : 3 .  What is the difference (in years) in their present ages?

20 years

Mother     :     Daughter

   5           :          3      ←  (present time)

   4           :          3      ←  (after 30 years)

ATQ,

⇒ \(\frac{5R + 30}{3R + 30}\) = \(\frac{4}{3}\)

⇒ 15R + 90 = 12R + 120

⇒ 3R = 30

⇒ 1R = 10

Therefore, Difference of their present age = 5R - 3R = 2R = 2 × 10 = 20 years