Question Detail

A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.

1 km/hr
2 km/hr
3 km/hr
4 km/hr

Answer: Option A

Explanation:

First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]

So we need to calculate speed downstream and speed upstream first.

Speed = Distance / Time [important]

\begin{aligned}
\text {Speed upstream =}\\ (\frac{15}{3\frac{3}{4}}) km/hr \\
= 15 \times \frac{4}{15} = 4 km/hr \\

\text{Speed Downstream = }
(\frac{5}{2\frac{1}{2}}) km/hr \\
= 5 \times \frac{2}{5} = 2 km/hr \\
\text {So speed of current = } \frac{1}{2}(4-2) \\
= 1 km/hr
\end{aligned}

1. A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed against the current will be

11 kmph
12 kmph
14 kmph
17 kmph

Answer: Option C

Explanation:

If you solved this question yourself, then trust me you have a all very clear with the basics of this chapter.

If not then lets solve this together.

Speed with current is 20,
speed of the man + It is speed of the current
Speed in still water = 20 - 3 = 17

Now speed against the current will be
speed of the man - speed of the current
= 17 - 3 = 14 kmph

2. 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}

3. In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still water

Answer: Option C

Explanation:

We know we can calculate it by 1/2(a+b)

=> 1/2(11+5) = 1/2(16) = 8 km/hr

4. A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.

.4 km
1.4 km
2.4 km
3.4 km

Answer: Option C

Explanation:

Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 - 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]
=> 2x + 3x = 12
=> x = 12/5 = 2.4 km

5. 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