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?
Option 1: 32
Option 2: 82
Option 3: 41
Option 4: 56
Correct Answer: 41
Solution : Let the present age of A is denoted as $a$ and B as $b$. Seven years ago, the ratio of the ages of A and B ⇒ $\frac{a - 7}{b - 7} = \frac{4}{5}$ ⇒ $5(a - 7) = 4(b - 7)$ ⇒ $5a-35=4b-28$ ⇒ $5a - 4b = 7$...............................(1) Eight years hence, the ratio of the ages of A and B ⇒ $\frac{a + 8}{b + 8} = \frac{9}{10}$ ⇒ $10(a + 8) = 9(b + 8)$ ⇒ $10a+ 80 = 9b + 72$ ⇒ $10a-9b = - 8$....................................(2) Multiplying Equation (1) by 2 and subtracting from Equation (2), We get $b=22$ and $a = 19$ $\therefore$ Sum of their present ages is $a + b = 19 + 22 = 41$ Hence, the correct answer is 41 years.
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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 difference between their present ages in years?
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