Theory & Concepts
SSC CGL Boats and Streams Questions, Formulas & Tricks
Prepare Boats and Streams for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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Practice Notes
15 min readDifficulty: Intermediate
Boats and streams is a subset of the speed, distance, and time chapter, focusing specifically on how the movement of water (the stream) affects the speed of the boat.
The core of this topic lies in understanding the two primary directions: moving with the flow (downstream) and moving against the flow (upstream). Mastering these two speed adjustments is enough to solve most CGL questions.
Learning path
- Defining upstream & downstream
- Speed of boat vs stream
- The master formulas
- 10 standard solved problems
- Round-trip logic
1. Fundamental formulas
Let be the speed of the boat in still water and be the speed of the stream.
Downstream Speed (D):
Upstream Speed (U):
Speed of Boat in Still Water (u):
Speed of Stream (v):
2. Solved examples
Question 01Standard pattern
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
4 hours
3 hours
5 hours
4.5 hours
Correct answer: a) 4 hours
Solution
Speed in still water \( u = 13 \text{ km/hr} \).
Speed of stream \( v = 4 \text{ km/hr} \).
Downstream speed \( D = u + v = 13 + 4 = 17 \text{ km/hr} \).
Time = \( \text{Distance} / \text{Speed} = 68 / 17 = 4 \text{ hours} \).
Question 02Standard pattern
In one hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
8 km/hr
6 km/hr
9 km/hr
7.5 km/hr
Correct answer: a) 8 km/hr
Solution
Downstream speed \( D = 11 \text{ km/hr} \).
Upstream speed \( U = 5 \text{ km/hr} \).
Speed in still water \( u = \frac{1}{2}(D + U) = \frac{1}{2}(11 + 5) \).
Calculation: \( \frac{16}{2} = 8 \text{ km/hr} \).
Question 03Standard pattern
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
1 hour 15 min
1 hour
1 hour 30 min
2 hours
Correct answer: a) 1 hour 15 min
Solution
Upstream speed \( U = 2 \text{ km/hr} \).
Downstream speed \( D = 1 \text{ km / (10/60)} = 6 \text{ km/hr} \).
Speed in still water \( u = \frac{1}{2}(2 + 6) = 4 \text{ km/hr} \).
Time for 5 km = \( 5 / 4 = 1.25 \text{ hours} = 1 \text{ hour } 15 \text{ min} \).
Question 04Standard pattern
A motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
5 km/hr
4 km/hr
6 km/hr
10 km/hr
Correct answer: a) 5 km/hr
Solution
Let speed of stream be \( v \).
Total time = \( \frac{30}{15 + v} + \frac{30}{15 - v} = 4.5 \text{ hours} \).
Multiply by \( (225 - v^2) \): \( 30(15 - v) + 30(15 + v) = 4.5(225 - v^2) \).
\( 900 = 4.5(225 - v^2) \implies 200 = 225 - v^2 \).
Result: \( v^2 = 25 \implies v = 5 \text{ km/hr} \).
Question 05Standard pattern
A man can row upstream at 7 km/hr and downstream at 10 km/hr. Find the man's rate in still water and the rate of current.
8.5 and 1.5 km/hr
7.5 and 2.5 km/hr
9 and 1 km/hr
8 and 2 km/hr
Correct answer: a) 8.5 and 1.5 km/hr
Solution
Speed in still water \( u = \frac{10 + 7}{2} = 8.5 \text{ km/hr} \).
Speed of current \( v = \frac{10 - 7}{2} = 1.5 \text{ km/hr} \).
Question 06Standard pattern
A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 km in 6 minutes. The speed of the stream is:
2 km/hr
1 km/hr
4 km/hr
3 km/hr
Correct answer: a) 2 km/hr
Solution
Upstream speed \( U = 60/10 = 6 \text{ km/hr} \).
Downstream speed \( D = 60/6 = 10 \text{ km/hr} \).
Speed of stream \( v = \frac{10 - 6}{2} = 2 \text{ km/hr} \).
Question 07Standard pattern
The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
3.6 km
3 km
4.2 km
2.4 km
Correct answer: a) 3.6 km
Solution
Downstream speed \( D = 15 + 3 = 18 \text{ km/hr} \).
Time = \( 12/60 = 0.2 \text{ hour} \).
Distance = \( 18 \times 0.2 = 3.6 \text{ km} \).
Question 08Standard pattern
A boat goes 6 km in an hour in still water but takes thrice as much time in going the same distance against the current. The speed of the current (in km/hr) is:
4 km/hr
2 km/hr
3 km/hr
5 km/hr
Correct answer: a) 4 km/hr
Solution
Speed in still water \( u = 6 \text{ km/hr} \).
Time against current = \( 3 \times 1 = 3 \text{ hours} \).
Upstream speed \( U = 6/3 = 2 \text{ km/hr} \).
Since \( U = u - v \implies 2 = 6 - v \).
Result: \( v = 4 \text{ km/hr} \).
Question 09Standard pattern
A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
1 km/hr
2 km/hr
1.5 km/hr
0.5 km/hr
Correct answer: a) 1 km/hr
Solution
Ratio of \( D : U = 4 : 3 \).
Let \( D = 4k, U = 3k \).
Total time: \( \frac{48}{4k} + \frac{48}{3k} = 14 \).
\( \frac{12}{k} + \frac{16}{k} = 14 \implies \frac{28}{k} = 14 \implies k = 2 \).
\( D = 8, U = 6 \text{ km/hr} \).
Rate of stream \( v = \frac{8 - 6}{2} = 1 \text{ km/hr} \).
Question 010Standard pattern
Two boats A and B start from opposite sides of a 100 km wide river. A goes at 15 km/hr in still water, B at 10 km/hr in still water. If the stream flows at 2 km/hr, after how long will they meet?
4 hours
5 hours
3 hours
2.5 hours
Correct answer: a) 4 hours
Solution
Relative speed (Opposite direction with stream) = \( (u_A + v) + (u_B - v) = u_A + u_B \).
The stream speed cancels out.
Net speed = \( 15 + 10 = 25 \text{ km/hr} \).
Time = \( 100 / 25 = 4 \text{ hours} \).