A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

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}

Answer: Option B

Explanation:

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = (9/54) hour
= (1/6)*60 minutes
= 10 minutes

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 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

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