Question 1

A boat takes 8 hours to travel 96 km downstream and 12 hours to travel the same distance upstream. Find the speed of the boat in still water.

Accepted Answer

Step 1: Let speed of boat in still water = b km/h and speed of stream = s km/h.

Step 2: Downstream speed = b + s, Upstream speed = b - s.

Step 3: From downstream: Distance = Speed × Time → 96 = (b + s) × 8 → b + s = 12 km/h.

Step 4: From upstream: 96 = (b - s) × 12 → b - s = 8 km/h.

Step 5: Adding both equations: (b + s) + (b - s) = 12 + 8 → 2b = 20 → b = 10 km/h.

Step 6: Subtracting: (b + s) - (b - s) = 12 - 8 → 2s = 4 → s = 2 km/h.

Verification: Downstream = 10 + 2 = 12 km/h; Time = 96/12 = 8 hours ✓. Upstream = 10 - 2 = 8 km/h; Time = 96/8 = 12 hours ✓.

Therefore, the speed of the boat in still water is 10 km/h.

Question 2

A boat can travel 20 km downstream in 2 hours and 20 km upstream in 4 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 20/2 = 10 km/h. Step 2: Upstream speed = 20/4 = 5 km/h. Step 3: Speed of boat in still water = (Downstream + Upstream) / 2 = (10 + 5) / 2 = 15/2 = 7.5 km/h. Therefore, answer is 7.5 km/h.

Question 3

A boat takes 6 hours to travel 120 km downstream and 8 hours to travel the same distance upstream. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 120 ÷ 6 = 20 km/h. Step 2: Upstream speed = 120 ÷ 8 = 15 km/h. Step 3: Speed of stream = (Downstream speed − Upstream speed) ÷ 2 = (20 − 15) ÷ 2 = 5 ÷ 2 = 2.5 km/h.

Question 4

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 5

A man can row 24 km downstream in 2 hours. If his speed in still water is 8 km/h, what is the speed of the current?

Accepted Answer

Step 1: Downstream speed = 24 ÷ 2 = 12 km/h. Step 2: Downstream speed = Man's speed + Current speed, so 12 = 8 + Current speed. Step 3: Current speed = 12 − 8 = 4 km/h.

Question 6

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 56 km upstream?

Accepted Answer

Step 1: Upstream speed = Boat speed − Stream speed = 10 − 3 = 7 km/h. Step 2: Time = Distance ÷ Speed = 56 ÷ 7 = 8 hours.

Question 7

A boat takes 4 hours to travel 60 km downstream and 6 hours to travel the same distance upstream. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 60 ÷ 4 = 15 km/h. Step 2: Upstream speed = 60 ÷ 6 = 10 km/h. Step 3: Stream speed = (Downstream speed − Upstream speed) ÷ 2 = (15 − 10) ÷ 2 = 5 ÷ 2 = 2.5 km/h.

Question 8

A boat travels 36 km upstream in 4 hours. If the current's speed is 1 km/h, what is the boat's speed in still water?

Accepted Answer

Step 1: Upstream speed = 36 ÷ 4 = 9 km/h. Step 2: Upstream speed = Boat speed − Current speed, so 9 = Boat speed − 1. Step 3: Boat speed = 9 + 1 = 10 km/h.

Question 9

A boat's speed in still water is 15 km/h. It takes 2 hours to travel downstream and 3 hours to travel upstream over the same distance. What is the distance?

Accepted Answer

Step 1: Let stream speed = s km/h. Downstream speed = 15 + s, Upstream speed = 15 − s. Step 2: Distance downstream = (15 + s) × 2, Distance upstream = (15 − s) × 3. Step 3: Since distances are equal: (15 + s) × 2 = (15 − s) × 3. Step 4: 30 + 2s = 45 − 3s. Step 5: 5s = 15, so s = 3 km/h. Step 6: Distance = (15 + 3) × 2 = 18 × 2 = 36 km.

Question 10

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 = Speed of boat − Speed of stream = 10 − 3 = 7 km/h. Step 2: Time = Distance ÷ Speed = 91 ÷ 7 = 13 hours.

Question 11

A man can row 30 km upstream in 5 hours. If the speed of the stream is 2 km/h, what is the speed of the man in still water?

Accepted Answer

Step 1: Upstream speed = Distance ÷ Time = 30 ÷ 5 = 6 km/h. Step 2: Upstream speed = Boat speed − Stream speed. Step 3: 6 = Boat speed − 2. Step 4: Boat speed = 6 + 2 = 8 km/h.

Question 12

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, find 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 13

A boat's speed in still water is 20 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 distance = d and stream speed = s. Step 2: Downstream: d = (20 + s) × 2. Step 3: Upstream: d = (20 − s) × 3. Step 4: Equate both: (20 + s) × 2 = (20 − s) × 3. Step 5: 40 + 2s = 60 − 3s. Step 6: 5s = 20. Step 7: s = 4 km/h.

Question 14

A man rows a boat 36 km downstream and 24 km upstream, taking 6 hours for the entire journey. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Accepted Answer

Step 1: Let boat speed = b km/h. Downstream speed = (b + 2), Upstream speed = (b - 2). Step 2: Total time equation: 36/(b+2) + 24/(b-2) = 6. Step 3: Multiply through by (b+2)(b-2): 36(b-2) + 24(b+2) = 6(b²-4). Step 4: 36b - 72 + 24b + 48 = 6b² - 24. Step 5: 60b - 24 = 6b² - 24. Step 6: 6b² - 60b = 0 → b(b - 10) = 0. Step 7: b = 10 km/h (b ≠ 0).

Question 15

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

Question 16

A boat travels from point A to point B (downstream) in 5 hours and from B to A (upstream) in 7.5 hours. If a person can swim at 12 km/h in still water, and the boat's speed in still water equals the swimmer's speed, what is the distance between A and B?

Accepted Answer

Step 1: Let distance = d km, stream speed = s km/h. Boat speed in still water = 12 km/h. Step 2: Downstream: d/(12+s) = 5, so d = 5(12+s) = 60 + 5s. Step 3: Upstream: d/(12-s) = 7.5, so d = 7.5(12-s) = 90 - 7.5s. Step 4: Equate: 60 + 5s = 90 - 7.5s. Step 5: 12.5s = 30, s = 2.4 km/h. Step 6: d = 60 + 5(2.4) = 60 + 12 = 72 km.

Question 17

A boat takes 10 hours to travel 120 km downstream. If the boat's speed in still water is 50% more than the stream's speed, how long will it take to travel 120 km upstream?

Accepted Answer

Step 1: Downstream speed = 120/10 = 12 km/h. Step 2: Let stream speed = s km/h. Then boat speed b = 1.5s. Step 3: Downstream: b + s = 12, so 1.5s + s = 12, thus 2.5s = 12, giving s = 4.8 km/h. Step 4: Boat speed b = 1.5 × 4.8 = 7.2 km/h. Step 5: Upstream speed = b - s = 7.2 - 4.8 = 2.4 km/h. Step 6: Time upstream = 120/2.4 = 50 hours.

Question 18

A boat takes 4 hours to travel 60 km downstream. If the ratio of the boat's speed in still water to the stream's speed is 5:1, how many hours will it take for the boat to travel 50 km upstream?

Accepted Answer

Step 1: Downstream speed = 60/4 = 15 km/h. Step 2: Let boat speed = 5x and stream speed = x. Then 5x + x = 15, so 6x = 15, x = 2.5. Boat speed = 12.5 km/h, stream speed = 2.5 km/h. Step 3: Upstream speed = 12.5 - 2.5 = 10 km/h. Step 4: Time upstream = 50/10 = 5 hours.

Question 19

A boat covers a certain distance downstream in 6 hours. The same distance upstream takes 9 hours. If the boat's speed in still water is 15 km/h, what is the distance?

Accepted Answer

Step 1: Let distance = D km, stream speed = s km/h, boat speed = 15 km/h. Step 2: Downstream: D/(15+s) = 6, so D = 6(15+s) = 90 + 6s. Step 3: Upstream: D/(15-s) = 9, so D = 9(15-s) = 135 - 9s. Step 4: Equate: 90 + 6s = 135 - 9s, so 15s = 45, thus s = 3 km/h. Step 5: D = 90 + 6(3) = 90 + 18 = 108 km.

SSC CHSL Boats & Streams

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Boats & Streams— Rules & Concept

Key Points to Remember

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Boats & Streams — Practice Questions

60-Second Revision — Boats & Streams