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The age gap between A and C is twice that between A and B. A is older than B and the ratio of the maximum and minimum possible age of C is 7 : 1. What is the ratio of the age of A to B?
  • a)
    8 : 7
  • b)
    4 : 3
  • c)
    3 : 2
  • d)
    8 : 5
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The age gap between A and C is twice that between A and B. A is older ...

Given Information:
- Age gap between A and C is twice that between A and B
- A is older than B
- Ratio of maximum and minimum possible age of C is 7 : 1

Let's Solve the Problem:

Step 1: Understanding the Age Gap
- Let's assume the age of A is x years, B is y years, and C is z years.
- According to the given information, the age gap between A and C is twice that between A and B. This can be represented as z - x = 2(x - y).

Step 2: Understanding the Ratio
- The ratio of the maximum and minimum possible age of C is 7 : 1. This implies that z = 7k and z = k for some positive integer k.

Step 3: Solving the Equations
- Substituting z = 7k and z = k in the equation z - x = 2(x - y), we get 7k - x = 2(x - y) and k - x = 2(x - y).
- Solving these two equations simultaneously, we find k = 3x and x = 2y.

Step 4: Finding the Ratio of Ages
- Since x = 2y, the ratio of the age of A to B is 2 : 1.
- Therefore, the ratio of the age of A to B is 8 : 4, which simplifies to 2 : 1 or 8 : 4 (dividing both by 2).
- Hence, the correct answer is option 'D' - 8 : 5.
Free Test
Community Answer
The age gap between A and C is twice that between A and B. A is older ...
Let the age of B = z
Age of A = z + x
Age of C = z + x + 2x or z + x – 2x
z + 3x or z – x
z + 3x : z – x = 7 : 1
z : x = 5 : 3
Ratio of the age of A : B = z + x : z = (5 + 3) : 5 = 8 : 5
Hence, Option D is correct.
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The age gap between A and C is twice that between A and B. A is older than B and the ratio of the maximum and minimum possible age of C is 7 : 1. What is the ratio of the age of A to B?a)8 : 7b)4 : 3c)3 : 2d)8 : 5Correct answer is option 'D'. Can you explain this answer?
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