Correct Answer - Option 3 : 264 m

**Concept:**

\(\text{Length of Curve} = R × δ×\frac{\pi}{180}\)

Where,

R = radius of curve, \(\delta\) = deflection angle

**Calculation:**

Given,

Length of chain = 20 m,

R = 15 chains = 15 × 20 = 300 m,

deflection angle (\(\delta \)) = 50°30' = 50.50° (∵ 1° = 60', So, 30' = 0.5°)

∵ We know that, \(\text{Length of Curve} = R × δ×\frac{\pi}{180}\)

⇒ \(\text{Length of Curve} = 300 × 50.50×\frac{\pi}{180}\)

∴ **Length of curve = 264.28 m**

The degree of curve is given as,

- For 20 m chain length, \(D_a = \frac{1146}{R}\)
- For 30 m chain length, \(D_a = \frac{1718}{R}\)

Where,

D_{a} = degree of curve and R = radius of the curve