The ratio of the ages of A and B, four years ago, was 4 : 5. Eight years hence, the ratio of the ages of A and B will be 11 : 13. What is the ratio of their present ages?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 9 : 11.
Let the present ages of A and B be x and y years respectively
According to the question
⇒ (x - 4)/(y - 4) = 4/5
⇒ 5 × (x - 4) = 4 × (y - 4)
⇒ 5x - 4y = 20 - 16
⇒ 5x - 4y = 4 .........(1)
Now, After 8 years
⇒ (x + 8)/(y + 8) = 11/13
⇒ 13 × (x + 8) = 11 × (y + 8)
⇒ 13x - 11y = 88 - 104
⇒ 13x - 11y = -16 .............(2)
After solving the equation (1) and (2)
⇒ x = 36 & y = 44
Hence, the required ratio = 36 : 44 = 9 : 11