Multiple choice

Ages of Amit and Gaurav are in the ratio 5 : 3. Ratio of age of Amit 4 years ago and Gaurav 4 years in future is 1 : 1. Find the ratio of the age of Amit 4 years in future and Gaurav 4 years ago.

  1. 3 : 1

  2. 2 : 1

  3. 4 : 1

  4. 2 : 5

  5. 3 : 7
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A Correct answer
Explanation

A/G = 5/3. A = 5x, G = 3x. (5x-4)/(3x+4) = 1/1. 5x-4 = 3x+4. 2x = 8. x = 4. A = 20, G = 12. Ratio (A+4)/(G-4) = 24/8 = 3/1.

AI explanation

Let the present ages of Amit and Gaurav be 5x and 3x. Four years ago, Amit's age was 5x - 4, and four years in the future, Gaurav's age will be 3x + 4. Setting these equal as given by the 1:1 ratio results in the equation 5x - 4 = 3x + 4. Solving for x gives 2x = 8, so x = 4. This makes Amit's present age 20 and Gaurav's present age 12, so Amit's age 4 years in the future (24) to Gaurav's age 4 years ago (8) results in the ratio 3:1.

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