Four years ago, the ratio of the ages of A and B was 3 : 4. Six years from now, the ratio of their ages will be 7 : 9. What is the sum of their present ages?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 148 years
Take the ages of four years ago as the unknowns; six years from now is 10 years after that time.
Four years ago: A \(=3k\), B \(=4k\)
\(\displaystyle \frac{3k+10}{4k+10}=\frac{7}{9}\)
\(9(3k+10)=7(4k+10)\), so \(27k+90=28k+70\) and \(k=20\)
A now \(=60+4=64\) years, B now \(=80+4=84\) years
Sum of present ages \(=64+84=148\) years