Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour ?

Answer: Option A

Explanation:

We know that,
$$\begin{aligned} Time = \frac{Distance}{Speed} \\ Speed = 20\text{ km/hr} = 20*\frac{5}{18}{ m/sec} \\ = \frac{50}{9}{ m/sec} \\ \text{ Time =} \left(400*\frac{9}{50}\right) \\ = 72 {sec} = 1\frac{1}{5}{ min} \end{aligned}$$

Answer: Option C

Explanation:

Relative speed between two = 6-1 = 5 round per hour

They will cross when one round will complete with relative speed,
which is 1/5 hour = 12 mins.

So 7:30 + 12 mins = 7:42

Answer: Option B

Explanation:

Important to Note first - Dead Head means - run or finish a race at exactly level or at same time.

From question it is clear that Ram runs faster than Sham by 25%,
So if Sham runs 100 meter in a given time then Ram will run 125 meter in that time.
So if Sham runs 4 meter then Ram will run 5 meter in given time (divide both by 25)
=> Ram can give Sham a lead of 1 meter in 5 meter race to finish race in dead heat.
Ratio of length of start given : length of race :: 1 : 5
As per question, start was given of 7 meter, So,
Length of race was 7 * 5 = 35.

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

Answer: Option A

Explanation:

Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr

Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4

So distance traveled on foot = 4(4) = 16 km