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Question Detail
A motorboat, whose speed in 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
- 2 km/hr
- 3 km/hr
- 4 km/hr
- 5 km/hr
Answer: Option D
Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr
So we know from question that it took 4(1/2)hrs to travel back to same point.
So,
\begin{aligned}
\frac{30}{15+x} - \frac{30}{15-x} = 4\frac{1}{2} \\
=> \frac{900}{225 - x^2} = \frac{9}{2} \\
=> 9x^2 = 225 \\
=> x = 5 km/hr
\end{aligned}
1. A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is
- 4 kmph
- 5 kmph
- 6 kmph
- 7 kmph
Answer: Option B
Explanation:
Rate upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.
= 25/18 m/sec
= (25/18)*(18/5) kmph
= 5 kmph
2. A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.
- 0,5
- 5,5
- 15,5
- 10,5
Answer: Option C
Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate in still water = 1/2(a+b)
Rate of current = 1/2(a-b)
=> Rate in still water = 1/2(20+10) = 15 kmph
=> Rate of current = 1/2(20-10) = 5 kmph
3. If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is
- 5 km/hr
- 4 km/hr
- 2 km/hr
- 1 km/hr
Answer: Option D
Explanation:
Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph
4. A man can row \begin{aligned} 9\frac{1}{3} \end{aligned} kmph in still water and finds that it takes him thrice as much time to row up than as to row, down the same distance in the river. The speed of the current is.
- \begin{aligned} 3\frac{2}{3}kmph \end{aligned}
- \begin{aligned} 4\frac{2}{3}kmph \end{aligned}
- \begin{aligned} 5\frac{2}{3}kmph \end{aligned}
- \begin{aligned} 6\frac{2}{3}kmph \end{aligned}
Answer: Option B
Explanation:
Friends first we should analyse quickly that what we need to calculate and what values we require to get it.
So here we need to get speed of current, for that we will need speed downstream and speed upstream, because we know
Speed of current = 1/2(a-b) [important]
Let the speed upstream = x kmph
Then speed downstream is = 3x kmph [as per question]
\begin{aligned}
\text{speed in still water = } \frac{1}{2}(a+b) \\
=> \frac{1}{2}(3x+x) \\
=> 2x \\
\text{ as per question we know, }\\
2x = 9\frac{1}{3} \\
=> 2x = \frac{28}{3} => x = \frac{14}{3} \\
\end{aligned}
So,
Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr.
Speed of the current \begin{aligned} =\frac{1}{2}[14 - \frac{14}{3}]\\
= \frac{14}{3}
= 4 \frac{2}{3} kmph \end{aligned}
5. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is
- 3:1
- 1:3
- 2:4
- 4:2
Answer: Option A
Explanation:
Let speed downstream = x kmph
Then Speed upstream = 2x kmph
So ratio will be,
(2x+x)/2 : (2x-x)/2
=> 3x/2 : x/2 => 3:1
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