Ram is 20 years older than Rahul. ‘n’ years ago Ram was thrice as old as Rahul. ‘2n’ years from now the ratio of the ages of Ram and Rahul will be 15 : 11. What is the value of ‘n’?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 15.
Let Ram's current age be R and Rahul's current age be r
Ram is 20 years older than Rahul
⇒ R = r + 20....(1)
n years ago, Ram was three times as old as Rahul
⇒ R - n = 3(r - n)....(2)
2n years from now, the ratio of their ages will be 15 : 11
⇒ (R + 2n)/(r + 2n) = 15/11....(3)
Put the value of R from equation 1 in equation 2
⇒ r + 20 - n = 3(r - n)
⇒ r + 20 = 3r - 3n + n
⇒ r + 20 = 3r - 2n
⇒ 2n + 20 = 2r
⇒ r = n + 10....(4)
Now, put R = (r + 20), and r = (n + 10) in equation 3
⇒ (r + 20 + 2n)/(r + 2n) = 15/11
⇒ (n + 10 + 20 + 2n)/(n + 10 + 2n) = 15/11
⇒ (3n + 30)/(3n + 10) = 15/11
⇒ 11(3n + 30) = 15(3n + 10)
⇒ 33n + 330 = 45n + 150
⇒ 45n - 33n = 330 - 150
⇒ 12n = 180
⇒ n = 15