Question 1

A boat covers 24 km upstream and 24 km downstream in a total of 10 hours. If the boat's speed in still water is 5 km/h, what is the speed of the stream?

Accepted Answer

Step 1: Let stream speed = s km/h. Upstream speed = 5 − s, Downstream speed = 5 + s. Step 2: Time upstream = 24 ÷ (5 − s), Time downstream = 24 ÷ (5 + s). Step 3: 24/(5−s) + 24/(5+s) = 10. Step 4: 24(5+s) + 24(5−s) = 10(5−s)(5+s). Step 5: 120 + 24s + 120 − 24s = 10(25 − s²). Step 6: 240 = 250 − 10s². Step 7: 10s² = 10, so s² = 1, thus s = 1 km/h.

Question 2

A boatman rows 30 km downstream in 2 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 30 ÷ 2 = 15 km/h. Step 2: Upstream speed = 30 ÷ 6 = 5 km/h. Step 3: Boat speed = (Downstream + Upstream) ÷ 2 = (15 + 5) ÷ 2 = 20 ÷ 2 = 10 km/h.

Question 3

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 4

A boat's speed in still water is 10 km/h and the stream 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 5

A man can row 36 km downstream in 4 hours and 32 km upstream in 8 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 36 ÷ 4 = 9 km/h. Step 2: Upstream speed = 32 ÷ 8 = 4 km/h. Step 3: Stream speed = (Downstream − Upstream) ÷ 2 = (9 − 4) ÷ 2 = 5 ÷ 2 = 2.5 km/h.

Question 6

The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How much time will the boat take to cover 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 7

A boat can travel 20 km upstream in the same time it takes to travel 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. Step 6: b = 25 km/h.

Question 8

A man rows a boat at a speed of 10 km/h in still water. The river flows at 2 km/h. If he rows 36 km downstream and then 36 km upstream, what is the average speed for the entire journey?

Accepted Answer

Step 1: Downstream speed = 10 + 2 = 12 km/h. Time downstream = 36/12 = 3 hours. Step 2: Upstream speed = 10 - 2 = 8 km/h. Time upstream = 36/8 = 4.5 hours. Step 3: Total distance = 36 + 36 = 72 km. Step 4: Total time = 3 + 4.5 = 7.5 hours. Step 5: Average speed = 72/7.5 = 9.6 km/h.

Question 9

A swimmer swims 24 km downstream in 2 hours and 24 km upstream in 4 hours. 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: Speed of current = (Downstream speed - Upstream speed)/2 = (12 - 6)/2 = 3 km/h.

Question 10

Two boats, A and B, start from the same point. Boat A travels downstream at a speed of 18 km/h (in still water speed 15 km/h), while Boat B travels upstream at a speed of 10 km/h (in still water speed 13 km/h). After 2 hours, Boat A turns around and travels upstream, while Boat B turns around and travels downstream. How much time will it take for them to meet after they turn around?

Accepted Answer

Step 1: From downstream and upstream speeds, find stream speed. For Boat A: 15 + s = 18, so s = 3 km/h. For Boat B: 13 - s = 10, so s = 3 km/h (consistent). Step 2: After 2 hours, Boat A has traveled 18 × 2 = 36 km downstream. Step 3: After 2 hours, Boat B has traveled 10 × 2 = 20 km upstream. Step 4: They are now 36 + 20 = 56 km apart. Step 5: After turning, Boat A travels upstream at 15 - 3 = 12 km/h. Step 6: After turning, Boat B travels downstream at 13 + 3 = 16 km/h. Step 7: They are now moving toward each other at a combined speed of 12 + 16 = 28 km/h. Step 8: Time to meet = 56 / 28 = 2 hours.

Question 11

A boat travels from Point P to Point Q (downstream) in 6 hours and returns from Q to P (upstream) in 9 hours. If the boat's speed in still water is 20 km/h, what is the distance between P and Q?

Accepted Answer

Step 1: Let distance = d km and stream speed = s km/h. Step 2: Downstream: d/(20+s) = 6, so d = 6(20+s) = 120 + 6s. Step 3: Upstream: d/(20-s) = 9, so d = 9(20-s) = 180 - 9s. Step 4: Equate: 120 + 6s = 180 - 9s. Step 5: 15s = 60, so s = 4 km/h. Step 6: d = 120 + 6(4) = 120 + 24 = 144 km. Step 7: Verify: Downstream speed = 20 + 4 = 24 km/h, time = 144/24 = 6 hours ✓. Upstream speed = 20 - 4 = 16 km/h, time = 144/16 = 9 hours ✓.

Question 12

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, what time will he take if his swimming speed is half that of the boat's speed in still water?

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 and s = 4 km/h (stream speed). Step 4: Man's speed in still water = 12/2 = 6 km/h. Step 5: Man's downstream speed = 6 + 4 = 10 km/h. Step 6: Time = 48/10 = 4.8 hours = 4 hours 48 minutes.

SSC CPO Boats & Streams

Boats & Streams— Rules & Concept

Key Points to Remember

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Boats & Streams — Practice Questions

60-Second Revision — Boats & Streams