A man covers half of his journey by train at 60 km/hr, half of the remaining by bus at 30 km/hr and the rest by cycle at 10 km/hr. Find his average speed during the entire journey?

Correct Answer: 100

Explanation:

Let the original speed  be x km/h, then

600 x - 600 x + 20 = 1 

 

? 600 x + 20 - x x x + 20 = 1  

 

? x 2 + 120 x - 12000 = 0

 

? x - 120 x - 100 = 0

 

Therefore,  original speed = 100km/h

Correct Answer: 120 km/hr

Explanation:

Number of gaps between 41 poles = 40
So total distance between 41 poles = 40*50
= 2000 meter = 2 km
In 1 minute train is moving 2 km/minute.
Speed in hour = 2*60 = 120 km/hour

Correct Answer: 10 km

Explanation:

Let distance = x km.
Time taken at 3 kmph : dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30-(-20) = 50 mins = 50/60 hours.
x/3- x/4 = 50/60
x/12 = 5/6
x = 10 km.

Correct Answer: 60 km/hr

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

Correct Answer: 8

Explanation:

Amy can travel clockwise or anticlockwise on the diagram.

Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

Similarly, anticlockwise she has four different routes.

Total routes = 8

Correct Answer: 7.5 min

Explanation:

B runs around the track in 10 min.

 i.e ,    Speed of B = 10 min per round

 Therefore,  A beats B by 1 round

  Time taken  by A to complete 4 rounds 

  = Time taken by B to complete 3 rounds  

 = 30 min 

 

Therefore, A's speed = 30/4 min per round = 7.5 min per round

 Hence, if the race is only of one round A's time over the course = 7 min 30 sec

Correct Answer: 3h

Explanation:

Time ( when X was 30 km ahead of Y) = (120-30)/20 =4.5h

Time ( when Y was 30 km ahead of X) = (120+30)/20 = 7.5 h

Thus, required  difference in time = 3h

Correct Answer: 55 kms

Explanation:

Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90 => x = 90 - y
But according to the question,
7x + 6y = 595
7(90-y) + 6y = 595
=> 630 - 7y + 6y = 595
=> y = 630 - 595 = 35
=> x = 90 - 35 = 55
Therefore, the distance travelled by taxi is 55 kms.

Correct Answer: 20 km

Explanation:

Average speed = 2 a b a + b, here a=25 b=4
= 2 x 25 x 4/(25+4) = 200/29 km/hr.

Distance covered in 5 hours 48 minutes
= Speed x time = (200/29)x (29/5) Distance covered in 5 hours 48 minutes = 40kms.

Distance of the post office from the village = (40/2) = 20 km.

Correct Answer: 4 kms

Explanation:

Let the actual distance be t kms

Now, According to the data,

 

$$\begin{gathered} 5 t + 8 60 = 6 t \\ = > 5 60 t + 8 60 = 6 t \\ = > 60 t + 8 = 72 t \\ = > 8 = 12 t \\ = > t = 8 / 12 = 2 / 3 hrs \end{gathered}$$

 

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.