A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 320 km of tour.

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:

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

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:

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.

$$\begin{aligned} Speed = \frac{Distance}{Time} \\ Distance = 650 meter \\ Time = \text{5 minutes} = 300 sec \\ Speed = \frac{600}{300} = 2 m/sec \\ => 2*\frac{18}{5} km/hr = 7.2 km/hr \end{aligned}$$

Answer: Option D

Explanation:

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