A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?

Answer: Option B

Explanation:

We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance.
Lets solve it.

Time = 50/60 hr = 5/6 hr
Speed = 48 mph
Distance = S*T = 48 * 5/6 = 40 km

New time will be 40 minutes so,
Time = 40/60 hr = 2/3 hr
Now we know,
Speed = Distance/Time
New speed = 40*3/2 kmph = 60kmph

Answer: Option A

Explanation:

We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9

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:

We know Time = Distance/speed

So total time taken =

$$\begin{aligned} \left(\frac{160}{64}+\frac{160}{80}\right) \\ = \frac{9}{2} hours \\ \text{ Time taken for 320 Km = } \\ 320*\frac{2}{9} = 71.11 km/hr \end{aligned}$$

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