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?
Option 1: 32
Option 2: 82
Option 3: 41
Option 4: 56
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 : The areas of the two triangles are in the ratio 4 : 3 and their heights are in the ratio 6 : 5. Find the ratio of their bases.
Option 1: 5 : 6
Option 2: 10 : 9
Option 3: 6 : 5
Option 4: 9 : 10
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
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