Explanation:

- Gyanendra and Arbind's ages are in the ratio 6:5.

- This means, their ages can be represented as 6x and 5x.

- The sum of their ages is given as 55 years. Thus, 6x + 5x = 55.

- Solving, we find x = 5. Therefore, Gyanendra is 30 years old, and Arbind is 25 years old.

- After seven years, Gyanendra will be 37 years old, and Arbind will be 32 years old.

- The new ratio of their ages will be 37:32.

- Let's examine the options:

- Option 1: 5:6

- Option 2: 37:32

- Option 3: 32:37

- Option 4: 6:5

Hence, the correct answer is Option 2: 37:32.

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