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### Question

The square root of twice my present age is equal to the sum of the square roots of my ages 10 years back and 10 years hence. What is my present age?

**A**

10 years.

**B**

11 years.

**C**

9 years.

**D**

20 years.

**Soln.**

**Ans: a**

Let the present age be x. Then $√(x - 10) + √(x + 10)$ = $√{2x}$. Squaring both sides, $(√(x - 10))^2 + (√(x + 10))^2 + 2√{x^2 - 10^2}$ = $2x$ which gives $x - 10 + x + 10 + 2√{x^2 - 10^2}$ = $2x$. Cancelling, and simplifying, $2√(x^2 - 100) = 0$, which leads to x = 10 years.