A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start at same point at 7:30 am. They shall first cross each other at ?

Answer: Option C

Explanation:

In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph

Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs

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

Answer: Option C

Explanation:

Let time taken to travel the first half = x hr
Then time taken to travel the second half = (10 - x) hr

Distance covered in the the first half = 21x [because, distance = time*speed]
Distance covered in the the second half = 24(10 - x)

Distance covered in the the first half = Distance covered in the the second half
So,
21x = 24(10 - x)
=> 45x = 240
=> x = 16/3

Total Distance = 2*21(16/3) = 224 Km [multiplied by 2 as 21x was distance of half way]

Answer: Option D

Explanation:

Let the speeds of two trains be 7X and 8X km/hr.

\begin{aligned}
8X = \frac{400}{4} \\
=> X = 12.5 Km/hr

\end{aligned}
So speed of first train is 12.5*7 = 87.5 km/hr

Answer: Option C

Explanation:

\begin{aligned}
Speed = \frac{Distance}{Time} \\
Distance = 750 meter \\
Time = \text{2 min 30 sec} = 150 sec \\
Speed = \frac{750}{150} = 5 m/sec \\

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