Question 1

A boat travels 72 km upstream in 9 hours. If the stream's speed is 1 km/h, what is the boat's speed in still water?

Accepted Answer

Step 1: Upstream speed = Distance ÷ Time = 72 ÷ 9 = 8 km/h. Step 2: Upstream speed = Boat speed − Stream speed, so 8 = Boat speed − 1. Step 3: Boat speed = 8 + 1 = 9 km/h.

Question 2

A boat's speed in still water is 10 km/h and the stream's speed is 3 km/h. How long will it take the boat to travel 91 km upstream?

Accepted Answer

Step 1: Upstream speed = Boat speed − Stream speed = 10 − 3 = 7 km/h. Step 2: Time = Distance ÷ Speed = 91 ÷ 7 = 13 hours.

Question 3

A boat takes 5 hours to travel 100 km downstream. If the boat's speed in still water is 18 km/h, what is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = Distance ÷ Time = 100 ÷ 5 = 20 km/h. Step 2: Downstream speed = Boat speed + Stream speed, so 20 = 18 + Stream speed. Step 3: Stream speed = 20 − 18 = 2 km/h.

Question 4

A boat's upstream speed is 12 km/h and its downstream speed is 18 km/h. What is the speed of the stream?

Accepted Answer

Step 1: Upstream speed = Boat speed − Stream speed = 12. Step 2: Downstream speed = Boat speed + Stream speed = 18. Step 3: Subtract equation 1 from equation 2: (Boat + Stream) − (Boat − Stream) = 18 − 12 → 2 × Stream speed = 6 → Stream speed = 3 km/h.

Question 5

A boat travels 48 km downstream in 3 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = Distance ÷ Time = 48 ÷ 3 = 16 km/h. Step 2: Downstream speed = Boat speed + Stream speed, so 16 = Boat speed + 2. Step 3: Boat speed = 16 − 2 = 14 km/h.

Question 6

A boat covers 60 km downstream and 40 km upstream in the same time. If the stream's speed is 5 km/h, find the boat's speed in still water.

Accepted Answer

Step 1: Let boat speed = b km/h. Downstream speed = (b + 5) km/h, Upstream speed = (b − 5) km/h. Step 2: Time is equal, so 60/(b+5) = 40/(b−5). Step 3: Cross-multiply: 60(b−5) = 40(b+5) → 60b − 300 = 40b + 200 → 20b = 500 → b = 25 km/h.

Question 7

A boat's speed in still water is 12 km/h. It takes 2 hours to travel a certain distance downstream and 3 hours to travel the same distance upstream. What is the speed of the stream?

Accepted Answer

Step 1: Let stream speed = s km/h. Downstream speed = (12 + s) km/h, Upstream speed = (12 - s) km/h. Step 2: Distance is same, so (12 + s) × 2 = (12 - s) × 3. Step 3: 24 + 2s = 36 - 3s. Step 4: 5s = 12, so s = 2.4 km/h.

Question 8

A swimmer swims 24 km downstream in 2 hours and 24 km upstream in 4 hours. If the swimmer swims at a constant speed in still water, what is the speed of the current?

Accepted Answer

Step 1: Downstream speed = 24 ÷ 2 = 12 km/h. Step 2: Upstream speed = 24 ÷ 4 = 6 km/h. Step 3: Swimmer's speed in still water = (12 + 6) ÷ 2 = 9 km/h. Step 4: Speed of current = (12 - 6) ÷ 2 = 3 km/h.

Question 9

The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How long will it take the boat to travel 72 km downstream and then return to the starting point?

Accepted Answer

Step 1: Downstream speed = 15 + 3 = 18 km/h. Step 2: Upstream speed = 15 - 3 = 12 km/h. Step 3: Time downstream = 72 ÷ 18 = 4 hours. Step 4: Time upstream = 72 ÷ 12 = 6 hours. Step 5: Total time = 4 + 6 = 10 hours.

Question 10

A boat can travel 20 km upstream in the same time it travels 30 km downstream. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

Accepted Answer

Step 1: Let boat speed = b km/h. Upstream speed = (b - 5) km/h, Downstream speed = (b + 5) km/h. Step 2: Time is equal, so 20/(b-5) = 30/(b+5). Step 3: Cross-multiply: 20(b+5) = 30(b-5). Step 4: 20b + 100 = 30b - 150. Step 5: 250 = 10b, so b = 25 km/h.

Question 11

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. A man swims at a constant speed in still water. If the man swims the same 48 km downstream, how long will it take him?

Accepted Answer

Step 1: Find boat's downstream speed = 48/3 = 16 km/h. Step 2: Find boat's upstream speed = 48/6 = 8 km/h. Step 3: Using (b+s) = 16 and (b-s) = 8, solve: 2b = 24, so b = 12 km/h (boat speed in still water). Step 4: Stream speed s = 16 - 12 = 4 km/h. Step 5: Man's speed in still water = 12 km/h (same as boat). Step 6: Man's downstream speed = 12 + 4 = 16 km/h. Step 7: Time = 48/16 = 3 hours.

Question 12

A boat travels 84 km downstream and returns upstream to the starting point. The downstream journey takes 4 hours and the upstream journey takes 7 hours. A swimmer with the same speed in still water as the boat takes 6 hours to swim 36 km in still water. What is the stream's speed?

Accepted Answer

Step 1: Boat's downstream speed = 84/4 = 21 km/h. Step 2: Boat's upstream speed = 84/7 = 12 km/h. Step 3: Boat's speed in still water = (21+12)/2 = 16.5 km/h. Step 4: Stream speed = (21-12)/2 = 4.5 km/h. Step 5: Swimmer's downstream speed = 99/6 = 16.5 km/h (matches boat's still-water speed + stream speed). Step 6: Stream speed = 4.5 km/h.

Question 13

A boat's speed in still water is 20 km/h. It travels 150 km downstream and then returns. If the total time taken is 16 hours, what is the speed of the stream? (Assume the boat travels at constant speed in still water throughout.)

Accepted Answer

Step 1: Let stream speed = s. Downstream speed = 20+s, upstream speed = 20-s. Step 2: 150/(20+s) + 150/(20-s) = 16. Step 3: Multiply by (20+s)(20-s): 150(20-s) + 150(20+s) = 16(400-s²). Step 4: 6000 = 6400 - 16s². Step 5: 16s² = 400 → s² = 25 → s = 5 km/h.

SSC MTS Boats & Streams

Boats & Streams— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Boats & Streams — Practice Questions

60-Second Revision — Boats & Streams