Divyansh's age is in the ratio 9 : 10 to the age of his sister Sara. Ten years ago, the ratio of their ages was 4 : 5. What is present age of Divyansh?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 18 years
Write the present ages with a common multiplier from the ratio 9 : 10; ten years ago both ages were 10 less, and they were then in the ratio 4 : 5.
Present ages: Divyansh \(9k\) years, Sara \(10k\) years
Ten years ago the ages were \(9k-10\) and \(10k-10\), in the ratio 4 : 5: \(\displaystyle\frac{9k-10}{10k-10}=\frac{4}{5}\)
\(45k-50=40k-40\), so \(5k=10\) and \(k=2\)
Divyansh's present age: \(9\times2=18\) years
Shortcut: Test the options; Divyansh's age must be a multiple of 9.
Only 18 is a multiple of 9, so \(k=2\) and Sara is 20