Twelve years ago the ratio of the ages of A and B was 12 5 Twelve years from now the ratio of their ...........

Quantitative Aptitude (MTS) Problems based on Ages

Twelve years ago, the ratio of the ages of A and B was 12 : 5. Twelve years from now, the ratio of their ages will be 18 : 11 . What is the difference between their present ages (in years)?

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SSC MTS 26th October 2021 Shift-2

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Explanation:

Correct option 1: 28 years
Given:
The ratio of the ages of A and B twelve years ago = 12:5
Twelve years from now, the ratio of their ages will be 18:11
Solution
Let, the age of A twelve years ago was = 12x
The age of B twelve years ago was = 5x
Total years between 'Twelve years ago from the present' and 'Twelve years after from present' = 12 + 12 = 24 years
Then, (12x + 24)/(5x + 24) = 18/11
⇒ 132x + 264 = 90x + 432
=132x-90x = 432-264
=42x = 168
⇒x= 168/42 = 4
.. The difference between their present ages = (12 x 4 +12) - (5 x 4+12)= 60-32 = 28 years