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.
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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 sum of their present ages in years?
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