Height and Distance (Railway Maths)

Total Questions: 57

1. A person 1.75 m tall casts a 2 m shadow. At the same instance, a lamp-post casts a shadow of 6.4 m. The height of the lamp-post is: [Group D 28/09/2022 (Morning)]

Correct Answer: (a) 5.6 m
Solution:

2. A man on a cliff observes a boat at an angle of depression of 30°, which is approaching the shore to a point exactly beneath the observer, at a uniform speed. Ten minutes later, the angle of depression of the boat is found to be 60°. Find the total time taken by the boat to reach the shore. [NTPC CBT II Level 6 (09/05/2022) Shift 2]

Correct Answer: (a) 15 minutes
Solution:

3. Two poles are on either side of a road. A 20m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against the other pole, it makes an angle of 30° with the road. Calculate the width of the road (in m) using √3 = 1.732) [NTPC CBT II Level 2 (16/06/2022) Shift 2]

Correct Answer: (d) 34.64
Solution:

4. Two walls of equal height are on either side of a road, which is 100 m wide. At a point on the road, two stairs are along the two walls in such a way that they indicate the two angles of elevation from the point 60° and 30°. The length of the larger stair is? [NTPC CBT - I 05/01/2021 (Evening)]

Correct Answer: (b) 50√3 m
Solution:

5. A bridge built across a river makes an angle of 45° with the river bank as shown in the given figure. If the length of the bridge is 150 m, then what is the width of the river? [NTPC CBT - I 11/01/2021 (Morning) ]

Correct Answer: (b) 75√2 m
Solution:

6. A 15m high tree is broken by the wind in such a way that its top touches the ground and makes an angle of 60° with the ground. At what height from the bottom is the tree broken? [NTPC CBT - I 11/01/2021 (Evening) ]

Correct Answer: (d)
Solution:

7. An observer 2 m tall is 150√3 m away from a tower. The angle of elevation from his eye to the top of the tower is 60°. The height of the tower is: [ NTPC CBT - I 16/01/2021 (Evening) ]

Correct Answer: (a) 452 m
Solution:

8. A small boy is standing at some distance from a flag post. When he sees the flag, the angle of elevation formed is 60°. If The height of the flag post is 30 feet, What is the distance of the boy from the flag post? [NTPC CBT - I 21/03/2021 (Morning)]

Correct Answer: (d) 10√3 ft
Solution:

9. Two ships are sailing in the sea on two sides of a lighthouse. The angles of elevation of top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 90 m high, then the distance between the two ships is________. [NTPC CBT - I 03/04/2021 (Morning) ]

Correct Answer: (b) 90(√3 + 1) m
Solution:

10. The angle of elevation of a hot-air balloon climbing vertically changes from 30° at 10:00 AM to 60° at 10:02 AM as observed from a point 300 m away from the take-off point. What is the upward speed of the balloon? [RRB JE 22/05/2019 (Evening)]

Correct Answer: (d) 2.9 m/s
Solution: