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Two men start together to walk a certain distance, one at 4 kmph and another at 3 kmph.The former arrives half an hour before the latter. Find the distance.

A.

6 km

B.

9 km

C.

8 km

D.

None of these

Answer with explanation

Answer: Option AExplanation

Let the distance be x km. Then,

x/3 – x/4 =1/2

(4x – 3x)/12 = 1/2

x = 6 km

Workspace

A.

60 km/hr

B.

90 km/hr

C.

120 km/hr

D.

135 km/hr

Answer

Workspace

A train leaves from a station and moves at a certain speed. After 2 hours, another train leaves from the same station and moves in the same direction at a speed of 60 mph. If it catches up with the first train in 4 hours, what is the speed of the first train?

A.

20 mph

B.

30 mph

C.

50 mph

D.

40 mph

Answer with explanation

Answer: Option DExplanation

Let the speed of the first train be ‘s’.

Distance covered by the first train in (2+4) hours = Distance covered by second train in 4 hours

Therefore, 6s = 60*4

Solving which gives s=40.

So the slower train is moving at the rate of 40 mph.

Workspace

A man travels at 3 mph in still water. If the current’s velocity is 1 mph, it takes 3 hours to row to a place and come back. How far is the place?

A.

3 miles

B.

7 miles

C.

5 miles

D.

4 miles

Answer with explanation

Answer: Option DExplanation

Let the distance be ‘d’ miles.

Time taken to cover the distance upstream + Time taken to cover the distance downstream = 3

Speed upstream = 3-1 = 2 mph

Speed downstream = 3+1 = 4 mph

So, our equation would be d/2 + d/4 = 3 → solving which, we get d = 4 miles.

Workspace

A bus travels at 54km/h while moving but after accounting for stopping time, to let passengers on and off the coach, it averages a speed of 45km/h. How many minutes does the bus stop for each hour?

A.

9 minutes

B.

8 minutes

C.

5 minutes

D.

10 minutes

Answer with explanation

Answer: Option DExplanation

In one hour without stopping, the bus would have travelled 54km. Once stopping is factored in, the bus actually travels 45km. So it travels 9km less far as a consequence.

Distance/Speed = Time

9km/54kmph = 0.16 hours

0.16 x 60 = 10 minutes

So the bus stops for ten minutes in every hour on average.

Workspace

A.

4 hours

B.

5 hours

C.

3 hours

D.

2 hours

Answer with explanation

Answer: Option DExplanation

Time taken to walk one side + Time taken to ride one side = 4 hours

Time taken to ride both sides = 2 x Time taken to walk one side = 6 hours

=> Time taken to walk one side = 3 hours

Therefore, time taken to ride one side = 4 – 3 = 1 hour

Thus, time taken to ride both sides = 2 x 1 = 2 hours

Workspace

A man decided to cover a distance of 6 km in 84 minutes. He decided to cover two thirds of the distance at 4 km / hr and the remaining at some different speed. Find the speed after the two third distance has been covered

A.

2 km / hr

B.

4 km / hr

C.

3 km / hr

D.

5 km / hr

Answer with explanation

Answer: Option DExplanation

We are given that two thirds of the 6 km was covered at 4 km / hr.

=> 4 km distance was covered at 4 km / hr.

=> Time taken to cover 4 km = 4 km / 4 km / hr = 1 hr = 60 minutes

=> Time left = 84 – 60 = 24 minutes

Now, the man has to cover remaining 2 km in 24 minutes or 24 / 60 = 0.4 hours

=> Speed required for remaining 2 km = 2 km / 0.4 hr = 5 km / hr

Workspace

A hare, pursued by a greyhound is 20 of her own leaps ahead of him. While the hare takes 4 leaps, the greyhound takes 3 leaps. 2 leaps of the greyhound is equal to 3 leaps of the hare. In how many leaps will the greyhound overtake the hare?

A.

180 leaps

B.

270 leaps

C.

360 leaps

D.

90 leaps

Answer with explanation

Answer: Option AExplanation

Workspace

A.

700 km

B.

740 km

C.

720 km

D.

760 km

Answer with explanation

Answer: Option CExplanation

Workspace

A thief steals a car and drives it at 15 km/hr. The theft has been discovered after one hour and the owner of the car sets off in another car at 25 km/hr. When will the owner overtake the thief from the starting point?

A.

1 hr

B.

1.5 hr

C.

2 hr

D.

2.5 hr

Answer with explanation

Answer: Option BExplanation

Workspace

Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?

A.

17 hr

B.

14 hr

C.

12 hr

D.

19 hr

Answer with explanation

Answer: Option AExplanation

relative speed =5.5−5=0.5=5.5−5=0.5 kmph (because they walk in the same direction)

distance =8.5=8.5 km

time=distancespeed=8.50.5=17 hr

Workspace

If a boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr, find his average speed for the entire trip?

A.

660/60km/hr

B.

60/61km/hr

C.

66 /61km/hr

D.

660/61km/hr

Answer with explanation

Answer: Option DExplanation

Time taken to cover 10 km = 10/12 hr = 5/6hr

time taken to cover 12 km = 12/10 hr = 6/5 hr

total distance travelled = 10+12km = 22km

total time taken = 6/5+5/6 hr

=61/30 hr

average speed = 22km / 61/30hr

=660/61km/hr

Workspace

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