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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)

here v is velocity in kmph, t is time in hours and 2 / 3 is value of 40 min in hour.

On solving we will get

t = 10 / 3 and

v = 12

So, distance = (10 / 3) * 12

= 40 kms

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

Then time taken to travel the second half = (10 - x) hr

Distance covered in the the first half = 21*x [because, distance = time*speed]

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

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

So, 21x = 24(10 - x)

=> 45x = 240

=> x = 16/3

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

QUESTION: 3

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 (∴ they walk in opposite directions) =2+3 = 5 rounds per hour

Therefore, 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

Hence they cross each other 7 times before 9.30 a.m

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:

If Arun doubles his speed, he needs 3 hour less.

Double speed means half time.

Hence, half of the time required by Arun to cover 30 km = 3 hour

i.e., Time required by Arun to cover 30 km = 6 hour

Arun's speed = 30 / 6 = 5 kmph

QUESTION: 5

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: 6

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 x 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 x 7 x (75 / 5) x 126

⇒ x = 35 km/hr

QUESTION: 7

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)hrs. = 9 / 2 hrs.

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

QUESTION: 8

**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: 9

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 questions we need to get the relative speed between them,

The relative speed of the boys = 5.5kmph – 5kmph

= 0.5 kmph

Distance between them is 8.5 km

Time = Distance/Speed

Time= 8.5km / 0.5 kmph = 17 hrs

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) m / sec

= 2 m/sec

= 2 x (18/5) km/hr

= 7.2 km/hr

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