Question : The ages of Gyanendra and Arbind are in the ratio 6 : 5. If the sum of their ages is 55 years, then what will be the ratio of their ages seven years from now?
Option 1: 5 : 6
Option 2: 37 : 32
Option 3: 32 : 37
Option 4: 6 : 5
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Correct Answer: 37 : 32
Solution :
Given: Ratio of Gyanendra and Arbind = 6 : 5
The sum of their ages = 55 years
Let the age of Gyanendra be $6x$ and the age of Arbind be $5x$.
According to the question,
⇒ $6x+5x=55$
⇒ $11x=55$
⇒ $x=5$
So, age of Gyanendra = 6 × 5 = 30 years
Age of Arbind = 5 × 5 = 25 years
After 7 years, ratio of their ages = (30 + 7) : (25 + 7)
= 37 : 32
Hence, the correct answer is 37 : 32.
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