# Vertical Alignment of Highways - IES Previous Year Questions

11. â€ƒA descending gradient of 4% meets an ascending gradient of 1 in 40 where a valley curve of length 200 m is to be formed. What will be the distance of the lowest point on the valley curve from its first tangent point ?

**[IES 2015]**

- 111 m
- 125 m
- 118 m
- 100 m

**Answer:**Option A

**Explanation:**

N

_{1}= - 0.04, N

_{2}= 1/40 = 0.025

Total deviation angle, N = | N

_{1}- N

_{2}| = |-0.04 - 0.025| = 0.065

Length of valley curve, L = 200 m

The distance of lowest point on the valley curve from its first tangent point is,

x = L x (N

_{1}/2N)

^{½}

⇒ x = 200 x {0.04 / (2 x 0.065)}

^{½}

⇒ x = 110. 94 m