Question Detail

A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.

4 hours
5 hours
6 hours
7 hours

Answer: Option A

Explanation:

It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.

Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph

Time = distance/speed = 84/21 = 4 hours

1. 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

2. 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

3. 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

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

4. 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

5. 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}