Question Detail

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

1. 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

2. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes ?

50 meter
100 meter
110 meter
None of above

Answer: Option B

Explanation:

Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr

Distance covered in 6 minutes =

$\begin{aligned} \frac{1}{60}*6 = \frac{1}{10} \\ = 100 meters \end{aligned}$

So distance between them after 6 minutes = 200 - 100
= 100 meters

3. An athlete runs 200 meters in 24 seconds. His speed is ?

10 km/hr
17 k/hr
27 km/hr
30 km/hr

Answer: Option D

Explanation:

$\begin{aligned} Speed = \frac{Distance}{Time} \\ = \frac{200}{24}m/sec = \frac{25}{3} m/sec \\ \frac{25}{3}*\frac{18}{5} km/hr = 30 km/hr \end{aligned}$

4. A car moves at 80 km/hr. What is the speed of the car in meters per second ?

$\begin{aligned} 20\frac{2}{9} m\sec \end{aligned}$
$\begin{aligned} 22\frac{2}{9} m\sec \end{aligned}$
$\begin{aligned} 24\frac{2}{9} m\sec \end{aligned}$
$\begin{aligned} 26\frac{2}{9} m\sec \end{aligned}$

Answer: Option B

Explanation:

$\begin{aligned} Speed = \left(80*\frac{5}{18}\right) m/sec \\ = \frac{200}{9} m/sec \\ = 22\frac{2}{9} m\sec \end{aligned}$

5. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.

50 km/hr
60 km/hr
65 km/hr
70 km/hr

Answer: Option B

Explanation:

We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.

Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km

New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph