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?
Option 1: 3
Option 2: 2
Option 3: 4
Option 4: 6
Question : The present ages of A and B are in the ratio 3 : 4. Twelve years ago, their ages were in the ratio 2 : 3. The sum of the present ages of A and B (in years) is:
Option 1: 72
Option 2: 60
Option 3: 84
Option 4: 48
Question : The present ages of A and B are in the ratio 5 : 6, respectively. After seven years this ratio becomes 6 : 7, then the present age of A in years is:
Option 1: 35 years
Option 2: 32 years
Option 3: 33 years
Option 4: 30 years
Question : Directions: The present ages of the three friends are in the proportions 6 : 7 : 8. Five years ago, the sum of their ages was 48 years. Find out their present ages in years.
Option 1: 24, 28, 32
Option 2: 18, 21, 24
Option 3: 30, 35, 40
Option 4: 12, 14, 16
Question : The ratio of a father's age to his son's age is 3 : 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
Option 1: 32 : 24
Option 2: 32 : 21
Option 3: 32 : 22
Option 4: 32 : 23
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