Answer: Option B
Let the age of Sohrab be x years, and the age of his father be y years. Then, according to the given information:

• y - x = 30 (the difference of their ages is 30)
• y^2 - x^2 = 1560 (the difference of the square of their ages is 1560)

We can use algebraic manipulation to solve for x and y. First, we can use the identity a^2 - b^2 = (a + b)(a - b) to simplify the second equation:

• (y + x)(y - x) = 1560

Substituting y - x = 30 from the first equation, we get:

• (y + x)(30) = 1560
• y + x = 52 (dividing both sides by 30)

Now we have two equations:

• y - x = 30
• y + x = 52

We can add these two equations to eliminate x:

• 2y = 82
• y = 41

Substituting y = 41 into either equation, we can solve for x:

• x = 11

Therefore, the age of Sohrab is 11 years, and the age of his father is 41 years. The correct answer is option B.
To summarize, the solution involves the following steps:

• Write down the equations based on the given information.
• Simplify the equations using algebraic manipulation.
• Solve for one variable in terms of the other.
• Substitute the solved variable into one of the equations to solve for the other variable.
• Verify the solution by checking that it satisfies both equations.