The ratio of the ages of Rohan and Sohan is 8 : 9. After 9 years, this ratio will become 19 : 21. If Arun is 3 years younger than Sohan, what is Arun's present age (in years)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 51
Find Sohan's age from the two ratios first; Arun's age follows from it.
Let Rohan \(=8x\) and Sohan \(=9x\)
\(\displaystyle \frac{8x+9}{9x+9}=\frac{19}{21}\)
\(21(8x+9)=19(9x+9)\), so \(168x+189=171x+171\)
\(3x=18\), so \(x=6\)
Sohan \(=9\times6=54\) years
Arun \(=54-3=51\) years