Ten years ago, the ratio of the ages of A and B was 4 : 5. Ten years hence, the ratio of their ages will be 6 : 7. If C is 10 years younger than B at present, what is the ratio of the present age of A to that of C?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 1
Write the ages of ten years ago with one unknown; ten years hence each is 20 years older than then.
Ten years ago: A \(=4k\), B \(=5k\) years
Ten years hence: \(\displaystyle \frac{4k+20}{5k+20}=\frac{6}{7}\)
\(7(4k+20)=6(5k+20)\), so \(28k+140=30k+120\) and \(k=10\)
Now: A \(=40+10=50\), B \(=50+10=60\) years
C \(=60-10=50\) years, so A : C \(=50:50=1:1\)