The ratio of the current ages of Ajay and Vijay is 7:4.The ratio between Ajay’s age 6 years ago and Vijay’s age 6 years from now is 1:1. Find the ratio between Ajay’s age 12 years hence and Vijay’s age 12 years ago.
Question
The ratio of the current ages of Ajay and Vijay is 7:4.The ratio between Ajay’s age 6 years ago and Vijay’s age 6 years from now is 1:1. Find the ratio between Ajay’s age 12 years hence and Vijay’s age 12 years ago.
Solution
Let's denote Ajay's current age as 7x and Vijay's current age as 4x, according to the first ratio given in the problem.
According to the second ratio, Ajay's age 6 years ago is equal to Vijay's age 6 years from now. This can be written as:
7x - 6 = 4x + 6
Solving this equation for x gives:
3x = 12 x = 4
So, Ajay's current age is 7x = 28 years and Vijay's current age is 4x = 16 years.
The problem asks for the ratio between Ajay’s age 12 years hence and Vijay’s age 12 years ago.
Ajay’s age 12 years hence is 28 + 12 = 40 years. Vijay’s age 12 years ago is 16 - 12 = 4 years.
Therefore, the ratio between Ajay’s age 12 years hence and Vijay’s age 12 years ago is 40:4 or 10:1.
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