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 D

Explanation:

Let the duration of the flight be x hours.
Then
$$\begin{aligned} \frac{600}{x}-\frac{600}{x + \frac{1}{2}} = 200 \\ \frac{600}{x}-\frac{1200}{2x+1} = 200 \\ x(2x+1) = 3 \\ 2x^2 + x - 3 = 0 \\ => (2x+3)(x-1)=0 \end{aligned}$$
Neglecting the negative value for x we get x = 1

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:

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 A

Explanation:

Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr

Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4

So distance traveled on foot = 4(4) = 16 km