Question Detail

A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

60 km/hr
100 km/hr
110 km/hr
120 km/hr

Answer: Option D

Explanation:

Number of gaps between 41 poles = 40
So total distance between 41 poles = 40*50
= 2000 meter = 2 km
In 1 minute train is moving 2 km/minute.
Speed in hour = 2*60 = 120 km/hour

1. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

9 km/hour
10 km/hour
11 km/hour
12 km/hour

Answer: Option D

Explanation:

We need to calculate the distance, then we can calculate the time and finally our answer.
Lets solve this,

Let the distance travelled by x km
Time = Distance/Speed

\begin{aligned}
\frac{x}{10} - \frac{x}{15} = 2 \\
\text{[because, 2 pm - 12 noon = 2 hours]} \\

3x - 2x = 60 \\
x = 60.

Time = \frac{Distance}{Speed} \\
Time @ 10km/hr = \frac{60}{10} = 6 hours

\end{aligned}
So 2 P.M. - 6 = 8 A.M
Robert starts at 8 A.M.

He have to reach at 1 P.M. i.e, in 5 hours

So, Speed = 60/5 = 12 km/hr

2. How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr

\begin{aligned} 1\frac{1}{5} min\end{aligned}
\begin{aligned} 2\frac{1}{5} min\end{aligned}
\begin{aligned} 3\frac{1}{5} min\end{aligned}
\begin{aligned} 4\frac{1}{5} min\end{aligned}

Answer: Option A

Explanation:

We know that,
\begin{aligned}
Time = \frac{Distance}{Speed} \\
Speed = 20\text{ km/hr} = 20*\frac{5}{18}{ m/sec} \\
= \frac{50}{9}{ m/sec} \\

\text{ Time =} \left(400*\frac{9}{50}\right) \\
= 72 {sec} = 1\frac{1}{5}{ min}
\end{aligned}

3. A person crosses a 600 meter long street in 5 minutes. What is the speed in Km/hr

6.2 km/hr
7.2 km/hr
8.2 km/hr
9.2 km/hr

Answer: Option B

Explanation:

Two things to give attention on this question.
First time is in minutes, we need to change it to seconds to get speed in m/sec, then we need to get the final answer in km/hr.
So lets solve this.

\begin{aligned}
Speed = \frac{Distance}{Time} \\
Distance = 650 meter \\
Time = \text{5 minutes} = 300 sec \\
Speed = \frac{600}{300} = 2 m/sec \\

=> 2*\frac{18}{5} km/hr = 7.2 km/hr
\end{aligned}

4. A train traveled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point.

6 hours 24 mins
6 hours 21 mins
6 hours 18 mins
6 hours 15 mins

Answer: Option B

Explanation:

Time taken to cover 600 km = 6 hours [because train speed is 100 km/hr]

Number of stops =
begin{aligned}
frac{600}{75} - 1 = 7 \
text{Total time on stops =}7*3 = 21 mins

end{aligned}
Total time taken by train = 6 hours 21 mins

5. A person travels equal distances with speed of 3 km/hr, 4 km/hr and 5 km/hr and takes a total of 47 minutes. Find the total distane

3 km
4 km
6 km
9 km

Answer: Option A

Explanation:

Let the distance be 3x km,
then,
\begin{aligned}
\frac{x}{3} +\frac{x}{4} +\frac{x}{5} = \frac{47}{60} \\
\frac{47x}{60} =\frac{47}{60} \\
x = 1
\end{aligned}
So total distance = 3*1 = 3 Km