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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

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.

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.