Question Detail

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

1. 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}

2. 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}

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. 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

5. 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