Question Detail

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

1. 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

2. Sahil can row 3 km against the stream in 20 minutes and he can return in 18 minutes. What is rate of current ?

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

Answer: Option A

Explanation:

\begin{aligned}
\text{Speed Upstream} = \frac{3}{\frac{20}{60}} = 9 km/hr \\
\text{Speed Downstream} = \frac{3}{\frac{18}{60}} = 10 km/hr \\
\text{Rate of current will be} \\
\frac{10-9}{2} = \frac{1}{2} km/hr
\end{aligned}

3. 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

4. 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}

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

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