The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?

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 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:

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 A

Explanation:

Let the distance be 3x km,
then,
$$\begin{aligned} \frac{x}{3} +\frac{x}{4} +\frac{x}{5} = \frac{47}{60} \\ \frac{47x}{60} =\frac{47}{60} \\ x = 1 \end{aligned}$$
So total distance = 3*1 = 3 Km

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