Question : 4 years ago, the age of Garvit was three times that of Yuvansh, but one year ago the age of Garvit was two times that of Yuvansh. What is the difference between the ages of Garvit and Yuvansh?
Option 1: 13 years
Option 2: 11 years
Option 3: 7 years
Option 4: 6 years
Correct Answer: 6 years
Solution :
Given,
4 years ago, the age of Garvit was three times that of Yuvansh, but one year ago the age of Garvit was two times that of Yuvansh.
Let the present age of Garvit be $x$ years and the present age of Yuvansh be $y$ years.
According to the question,
4 years ago
$x - 4 = 3 × (y - 4)$..........(1)
Also, one year ago,
$x - 1 = 2 × (y - 1)$............(2)
Subtracting (2) from (1),
⇒ $- 3 = y - 10$
⇒ $y = 7$
Substituting y = 7 in (1),
$x = 3 × (7 - 4) + 4 = 13$
⇒ The difference between the ages of Garvit and Yuvansh is 13 – 7 = 6 years
Hence, the correct answer is 6 years.
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