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. 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

3. 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}

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. 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}