SSC CGL (Prelims) Maths: Time, Speed and Distance questions with solutions

Q1. A boat covers a distance of 55 km downstream in 5 hours, while it takes 11 hours to cover the same distance upstream. What is the speed of the boat in still water?

1. 8 km/h
2. 9 km/h
3. 11 km/h
4. 7 km/h

Answer: 8 km/h

Downstream speed = $55/5=11$ km/h and upstream speed = $55/11=5$ km/h. Speed of the boat in still water is $\frac{11+5}{2}=8$ km/h.

Q2. A boat can go 54 km upstream in 6 hours. If the speed of the stream is 4.8 km/h, then how much time will the boat take to cover a distance of 279 km downstream?

1. 20
2. 15
3. 18
4. 16

Answer: 15

Upstream speed is \(54/6=9\) km/h. If stream speed is 4.8 km/h, then boat speed in still water is \(9+4.8=13.8\) km/h. Downstream speed is \(13.8+4.8=18.6\) km/h, so time for 279 km is \(279/18.6=15\) hours.

Q3. The speed of a boat in still water is 18 km/h and the speed of the stream is 3 km/h. How much time, in hours, will it take to cover a distance of 105 km downstream and then return upstream?

1. 12
2. 10
3. 15
4. 9 2/7

Answer: 12

Downstream speed = 18 + 3 = 21 km/h and upstream speed = 18 - 3 = 15 km/h. Time taken = $105/21 + 105/15 = 5 + 7 = 12$ hours.

Q4. The speed of a boat in still water is 12 km/h. If it can travel 30 km downstream in 2 hours, what is the speed of the stream?

1. 3 km/h
2. 2 km/h
3. 6 km/h
4. 5 km/h

Answer: 3 km/h

The downstream speed is 30/2 = 15 km/h. Since boat speed in still water is 12 km/h, the stream speed is 15 - 12 = 3 km/h.