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’?

Correct option is A

Given:
Ram is 20 years older than Rahul.
‘n’ years ago. Ram was thrice as old as Rahul
‘2n’ years from now, the ratio of ages of Ram and Rahul will be 15:11.
Solution:
Lets current age of Ram be R and Rahul be r
Then,
R= r+ 20 …(1)
R- n = 3(r-n)…..(2)
​$$\frac{R + 2n}{r + 2n} = \frac{15}{11} \, \dots (3)$$​​
From eq(1)
R=r+20
From eq (2)
R -n=3(r-n)
r+20-n=3r-3n
2r-2n =20
r-n=10
From eq(3)
​$$\frac{R + 2n}{r + 2n} = \frac{15}{11}\\11(R + 2n) = 15(r + 2n)\\11(r + 20 + 2n) = 15(r + 2n)\\11r + 220 + 22n = 15r + 30n\\220 = 4r + 8n\\55 = r + 2n\\$$​​
Now we have 2 equations
From r-n= 10
R= n+10
Substituting r in equation r+2n =55
(n+10) +2n =55
3n+10= 55
3n=45
n= 15