Question Detail

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

1. 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

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. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is

12 kmph
13 kmph
14 kmph
15 kmph

Answer: Option B

Explanation:

Rate upstream = (7/42)*60 kmh = 10 kmph.
Speed of stream = 3 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x-3 = 10 or x = 13 kmph

4. 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}

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}