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QUESTION: 1

A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?

Solution:

__According to given condition:__

- vt = (v + 3) (t - 2/3)
- vt = (v - 2) (t + 2/3)

On solving we will get:

t = 10/3 hrs and v = 12 km/hr

So, distance = (10/3) * 12 = 40 km

QUESTION: 2

A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

Solution:

Let time taken to travel the first half = x hr

⇒ Time taken to travel the second half = (10 - x) hr

∵ Distance = Time * Speed

Distance covered in the first half = 21x

Distance covered in the the second half = 24(10 - x)

∵ Distance covered in the the first half = Distance covered in the the second half

⇒ 21x = 24(10 - x)

⇒ 45x = 240

⇒ x = 16/3

Total Distance = 2 * 21(16/3) = 224 Km [∵ multiplied by 2 as 21x was the distance of half way]

QUESTION: 3

Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

Solution:

Due to stoppages, it covers 9 km less in an hour.

Time taken to cover 9 km =(9/54 )*60 min = 10 min.

QUESTION: 4

In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?

Solution:

Let Anil takes x hrs.

⇒ Arun takes x+2

If Arun doubles the speed, he will take x-1 hrs

⇒ He needs 3 hours less.

∵ **Double speed means half time**.

∴ Half of the time required by Arun to cover 30 km = 3 hours

⇒ Time required by Arun to cover 30 km = 6 hour

Thus, Arun's speed = 30/6 = 5 km/h

QUESTION: 5

A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?

Solution:

Relative speed = Speed of A + Speed of B = 2 + 3 = 5 rounds per hour

(∴ they walk in opposite directions)

⇒ They cross each other 5 times in 1 hour and 2 times in 1/2 hour

∵ Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour

∴ They cross each other 7 times before 9.30 a.m

QUESTION: 6

A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?

Solution:

Total time taken = (160/64) + (160/80) = 9/2 hrs

∴ Average speed = 320 x (2/9) = 71.11 km/hr.

QUESTION: 7

A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?

Solution:

Time taken = 1 hr 40 min 48 sec = 1 hr (40 + 4/5) min = 1 + 51/75 hrs = 126/75 hrs

Let the actual speed be x km/hr

Then, (5/7) * x * (126/75) = 42

⇒ x = 42 * 7 * (75 / 5) * 126

⇒ x = 35 km/hr

QUESTION: 8

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?

Solution:

In this type of question, we need to get the relative speed between them.

The relative speed of the boys = 5.5 – 5 = 0.5 km/h

The distance between them is 8.5 km.

Time = Distance/Speed

Time = 8.5/0.5 = 17 hrs

QUESTION: 9

**Q.** A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways, is:

Solution:

Given that time taken for riding both ways will be 2 hours lesser than the time needed for walking one way and riding back.

From this, we can understand that

**Time needed for riding one way = time needed for walking one way - 2 hours**

Given that time taken in walking one way and riding back = 5 hours 45 min

Hence, the time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min

QUESTION: 10

A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

Solution:

Speed = Distance/ Time

Speed = (600 / 5 x 60) = 2 m/s

**i.e. **Speed = 2 x (18/5) km/hr = 7.2 km/hr

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