Time Speed and Distance Questions for CAT

Question 1: I walk to a town at \(3_2^1\) kmph, rest there for 45 minutes and ride back at \(7_2^1\) kmph. Find the distance to the town, if the total time spent by me is 6 hrs 37 min.
[1] 14 km
[2] 7km
[3] 5 km
[4] 8 km

Answer:

Option: 1

Explanation:

Let the distance be D.

Therefore, \(\begin{array}{l}\frac{D}{{3.5}} + \frac{{45}}{{60}} + \frac{D}{{7.5}} = 6\frac{{37}}{{60}}\\ \Rightarrow D = 14\;cm\end{array}\)


Question 2: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in metres) is
[1] 45
[2] 54
[3] 50
[4] 72

Answer:

Option: 3

Explanation:

Let the length of train be x km and its speed be y km/hr.

Then, \(\frac{x}{{y - 2}} = \frac{9}{{60 \times 60}}{\rm{ and }}\frac{x}{{y - 4}} = \frac{{10}}{{60 \times 60}}\)

=> 9y – 3600x = 18 and 10y -3600x =40

=> y- 400x = 2 and y – 360x =4

Therefore, 40x = 2 or \(x\) m


Question 3: A man reaches his office 30 min late, if he walks from his home at 3 km per hour and reaches 40 min early if he walks at 4 km per hour. How far is his office from his house?
[1] 7km
[2] 14 km
[3] 5 km
[4] 3 km

Answer:

Option: 2

Explanation:

Time gained = 30 + 40 = 70 min =\(\frac{{70}}{{60}}\)hrs.

Let the distance be x km.

Therefore, \(\frac{x}{3} - \frac{x}{4} = 70 \times \frac{1}{{60}} \Rightarrow x = 14\) km


Question 4: Raju, walking at the rate of 6 kmph, covers a certain distance in three hours. In how much time will Raju cover this distance running at the speed of 18 kmph?
[1] 1 hour
[2] 3 hours
[3] 60 hours
[4] 22 hours

Answer:

Option: 1

Explanation:

Let the distance be X.

=>Distance = Speed x Time taken = 6 x 3 = 18 km.

Now, speed = 18 km/hr.

=>Time taken = Distance/Speed = 18/ 18 = 1 hour.


Question 5: Two cyclists start together to travel to a certain destination, one at the rate of 4 kmph and the other at the rate of 5 kmph. Find the distance if the former arrives half an hour after the latter.
[1] 2 km
[2] 10m
[3] 10000m
[4] 1 km

Answer:

Option: 3

Explanation:

Let the distance be X km. Now Time= distance/ speed.

=>Time for the first rider = X/14.

Similarly, time for the second cyclist = X/5.

Given that: X/14 – X/5 =1/2

=> X= 10 km = 10000 m



Time Speed and Distance

Time Speed and Distance Questions for CAT
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