Final answer:
After setting up algebraic equations and solving them, it's found that the son's present age is 22 years. Since this age does not match any of the given options in the question, there appears to be a typo or error in the options presented to the student.
Step-by-step explanation:
The student has asked a question that requires solving an age-related word problem using algebra. To find the present age of the son, we can set up equations based on the information given:
- Let the present age of the son be x years.
- Therefore, Damodar's present age is x + 26 years.
- In 4 years, the son's age will be x + 4 years.
- At that time, Damodar's age will be (x + 26) + 4 = x + 30 years.
- The problem states that in 4 years, Damodar's age will be twice the age of his son. So, x + 30 = 2(x + 4).
We can solve this equation to find the son's age:
- x + 30 = 2(x + 4)
- x + 30 = 2x + 8
- 30 - 8 = 2x - x
- 22 = x
So, the son's present age is 22 years. This seems to be a typo in the question as the options provided include ages 10, 12, 14, and 16 years, which are not correct based on the calculation. Therefore, the correct age based on the given problem and the solution mentioned above is not present in the options provided to the student.Let's assume that the present age of Damodar's son is x years.
According to the given information, Damodar is 26 years older than his son, so Damodar's age would be x + 26 years.
In 4 years, Damodar's age will be twice the age of his son. So, we can set up the equation x + 26 + 4 = 2(x + 4).
Simplifying the equation, we have x + 30 = 2x + 8.
By subtracting x from both sides, we get 30 = x + 8.
Subtracting 8 from both sides, we get 22 = x.
Therefore, the present age of Damodar's son is 22 years.