Let ages of Seema and her mother be “5x” years and “12x” years respectively.
Difference between ages is 21 years
Hence,
12x - 5x = 21
7x = 21
x = 3
Therefore,
Age of Seema = 5 × 3 = 15 years
Age of her mother = 12 × 3 = 36 years
Ratio of ages after three years = ( 15+3 ) / (36+3 )
= 18 / 39
= 6 / 13
= 6 : 13