5 years ago, the age of mother and her daughter was in ratio 3 : 1. 15 years hence, the ratio of their ages will be 13 : 7. What are their present ages ?

50 yrs , 20 yrs 

5 years ago:⇒   Age of mother : age of daughter = 3 : 1

15 years hence:⇒  Age of mother : age of daughter = (3R + 20) : (1R + 20)

Now, ATQ

⇒ \(\frac{3R\;+\;20}{1R\;+\;20}\) = \(\frac{13}{7}\)

⇒ 21R + 140 = 13R + 260

⇒ 8R = 120

⇒ 1R = 15

So,

Mother's present age = 3R + 5 = (15 × 3) + 5 = 45 + 5 = 50

Daughter's present age = 1R + 5 = (15 × 1) + 5 = 20