Question : Seven years ago, the ratio of the ages of A and B was 4 : 5. Eight years hence, the ratio of the ages of A and B will be 9 : 10. What is the difference between their present ages in years?
Option 1: 3
Option 2: 2
Option 3: 4
Option 4: 6
Correct Answer: 3
Solution :
Let the present ages of A and B as $a$ and $b$ respectively.
From the problem,
Seven years ago, the ratio of the ages of A and B was 4 : 5.
$⇒\frac{a-7}{b-7} = \frac{4}{5}$
$⇒5a - 35 = 4b - 28$
$⇒5a - 4b = 7$ ____(I)
Eight years hence, the ratio of the ages of A and B will be 9 : 10.
$⇒\frac{a+8}{b+8} = \frac{9}{10}$
$⇒10a + 80 = 9b + 72$
$⇒10a - 9b = - 8$ ____(II)
Solving these two equations simultaneously,
$⇒a = 19$
$⇒b = 22$
Therefore, the difference between their present ages = 22 - 19 = 3 years
Hence, the correct answer is 3.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
