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.

Answer: Option C

Explanation:

Speed while going = 40 km/hr
Speed while returning = 150% of 40 = 60 km/hr

Average speed =
$$\begin{aligned} \frac{2xy}{x+y} \\ = \frac{2*40*60}{40+60} = \frac{4800}{100} \\ = 48 Km/hr \end{aligned}$$

Answer: Option B

Explanation:

Suppose they meet x hrs after 8 a.m.
then
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
So, 60x+75(x-1) = 330

x=3.

So,they meet at (8+3). i.e 11a.m.

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 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:

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