Solution -
10 years ago,
The age of karishma = x
The age of Babita = 3x
The present age of Karishma = x + 10
The present age of Babita = 3x + 10
14 years hence,
The age of karishma = x + 10 + 14
= x + 24
The age of Babita = 3x + 10 + 14
= 3x + 24
The ratio of ages of Karishma and Babita = 5 : 9
(x + 24)/(3x + 24) = 5/9
9(x + 24) = 5(3x + 24)
9x + 126 = 15x + 120
216 - 120 = 15x - 9x
6x = 96
x = 96/6
x = 16
Thus,
The present age of Karishma = x + 10
= 16 + 10
= 26
The present age of Babita = 3x + 10
= 3(16) + 10
= 48 + 10
= 58
And,
The ratio of their present ages = 26 : 58
= 13 : 29
Hence,
The correct answer is option (a) 13 : 29.
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