10 years ago the age of Karishma was 1/3rd of the age of Babita.
Posted on 14-02-2023
Ques - 10 years ago the age of Karishma was 1/3rd of the age of Babita. 14 years hence the ratio of ages of Karishma and Babita will be 5 : 9. Find the ratio of their present ages :
(a) 13 : 29
(b) 11 : 27
(c) 29 : 17
(d) 13 : 25
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.
Thank You