Six years ago, the ratio of the ages of Preeti and Ruchi was 6 : 5. After four years, the ratio of their ages will be 11 : 10. What is Ruchi's present age?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 16 years
Take the ages six years ago with one unknown. From then to four years hence is 10 years, which is added to each age.
Six years ago: Preeti \(=6x\), Ruchi \(=5x\)
\(\displaystyle \frac{6x+10}{5x+10}=\frac{11}{10}\)
\(10(6x+10)=11(5x+10)\), so \(60x+100=55x+110\)
\(5x=10\), so \(x=2\)
Ruchi six years ago \(=10\), so Ruchi now \(=10+6=16\) years