A circular swimming pool is surrounded by a concrete wall 4 m wide. If the area of the concrete wall surrounding the pool is $$\frac{{11}}{{25}}$$ that of the pool, then the radius (in m) of the pool:

Solution (By Examveda Team)

Let the radius of swimming pool = R

Outer radius of pool with concrete wall = (R + 4)
According to question
πR² × $$\frac{{11}}{{25}}$$ = π(R + 4)² - πR²
R² × $$\frac{{11}}{{25}}$$ = R² + 16 + 8R - R²
$$\frac{{11}}{{25}}$$ R² = 16 + 8R
11R² - 200R - 400 = 0
By option (D), (In such type of equation go through the option to save your valuable time)
R = 20
11 × (20)² - 200 × 20 - 400 = 0
4400 - 4000 - 400 = 0
0 = 0 (satisfy)
Therefore, radius of pool R = 20 m