Question : Six years ago, the ratio of ages of A to B was 7 : 5. 4 years from now, the ratio of their ages will be 11 : 9. What is A’s age at present?
Option 1: $24 \frac{1}{2}$ years
Option 2: $22 \frac{1}{2}$ years
Option 3: $23 \frac{1}{2}$ years
Option 4: $21 \frac{1}{2}$ years
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Correct Answer: $23 \frac{1}{2}$ years
Solution :
Six years ago, the ratio of ages of A to B was 7 : 5.
Six years ago the ages of A and B were $7x$ and $5x$ respectively.
4 years from now, the ratio of their ages will be 11 : 9.
So, according to the question,
$\frac{7x+10}{5x+10}=\frac{11}{9}$
$⇒ 63x+90=55x+110$
$⇒8x=20$
$\therefore x = 2.5$
So A's present age = $7×2.5+6=23.5=23\frac{1}{2}$ years
Hence, the correct answer is $23\frac{1}{2}$ years.
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