Time Speed and Distance – 5/5Races and Circular Races

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Linear races

Concept of Head start:

In a race of X metres, if A gives B a head start of Y meters then B will start the

race Y metres ahead of A i.e. if A runs for entire X metres then B will only run

for X-Y metres.

In a race of X metres, if A gives B a head start of t seconds then A will start the

race t seconds after B.

1. In a race of 1000 m, A beats B by 200 m and B beats C by 200 m. By what

distance does A beat C?

(1) 400 m (2) 350 m

(3) 360 m (4) 380 m

2. In a race of 1000 m, A beats B by 200 m. In a race of 1500 m B beats C by 300 m.

By what distance will A beat C in a 2000 m race?

(1) 600 m (2) 700 m

(3) 720 m (4) 800 m

3. In a race of 1000 m, A beats B by 200 m or 20 seconds. What is the speed of A?

(1) 12.5 m/sec (2) 13 m/sec

(3) 15 m/sec (4) 11.5 m/sec

4. P beats Q by 20 m in a 120 m race, and Q beats R by 24 m in the same race. By

what distance will P beat R in a race of 150 m?

(1) 54 m (2) 50 m (3) 48 m (4) 45 m

5. In a 300 m race, the ratio of the speeds of two contestants A and B is 2 : 3. At a point

in the race, B was 60 m ahead of A. Find the distance covered by B then ?

(1) 180 m

(2) 120 m

(3) 240 m

(4) 220 m

6. In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 3. If A has a

head start of 170 m, then A wins by

(1) 5 m

(2) 10 m

(3) 15 m

(4) 20 m

7. Karan and Arjun run a 100-meter race, in which Karan beats Arjun by 10 metres. To

do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100

metre race. They both run at their earlier speeds. Which of the following is true in

connection with the second race?

(1) Karan and Arjun reach the finishing line simultaneously.

(2) Arjun beats Karan by 10 metres

(3) Arjun beats Karan by 11 metres.

(4) Karan beats Arjun by 1 metre.

8. Three runners A, B and C run a race, with runner A finishing 12 m ahead of runner B

and 18 m ahead of runner C, while runner B finishes 8 m ahead of runner C. Each

runner travels the entire distance at a constant speed. What was the length of the race?

[CAT 2001]

(1) 36 m (2) 48 m (3) 60 m (4) 72 m

Circular Races

When two persons are running around a circular track in the same direction, the difference

in the distances covered by the faster and slower person between two meeting points is

equal to the perimeter of the circular track and the relative speed is equal to difference in

speeds of two persons.

Circular Races

When two persons are running around a circular track in opposite directions, the relative

speed is equal to the sum of their speeds and from one meeting point to another, the sum of

the distances travelled by them is equal to the perimeter of circular track.

Circular Races

Two persons starting a race on a circular track at the same time and from the same point,

will meet for the first time when the faster person gains one complete round over the

slower person. The time taken for this = length of track / relative speed

Circular Races

Two persons starting a race on a circular track at the same time and from the same point,

will meet for the first time at the starting point after a time which is the LCM of time taken

by each one of them to complete one lap of the track.

Circular Races

Three persons starting a race on a circular track and from the same starting point, will meet

for the first time after the start at a time which is equal to the LCM of the time taken by the

fastest to gain a complete round over each of the other two.

1) A and B can run at 10m/s and 15 m/s respectively. They are running on a

800 m track . They start simultaneously from P. Find

a. The time it takes A and B to meet the first time after the start, if they run

in the same direction.

b. The time it takes A and B to meet the first time after the start, if they run in

the opposite direction.

In (a) and (b) When will they meet at P again for the first time. ?

2. A , B, C can run at 10m/s , 15 m/s, 20 m/s respectively. They are running on a

800 m track . They start simultaneously from P. Find

a. The time it takes A, B, C to meet the first time after the start, if they all run

in the same direction.

b. The time it takes A, B and C to meet the first time after the start, if A and B run

in the clock wise direction while C runs in the anticlockwise direction.

3. If A and B are running around a circular track of 500 m with speeds in the ratio

of 5:3, In how many distinct points would they meet, if they are start from same

point and in same direction ?

(1) 1 (2) 2 (3) 3 (4) 8

4. If A and B are running around a circular track of 500 m with speeds in the ratio

of 5:3, In how many distinct points would they meet, if they are start from same

point and in opposite direction ?

(1) 1 (2) 2 (3) 3 (4) 8

5. If A and B are running around a circular track of 500 m with speeds in the ratio

of 5:3, In how many distinct points would they meet, if they are start from a point

which is diametrically opposite to each other but in same direction ?

(1) 1 (2) 2 (3) 3 (4) 8

6. If A and B are running around a circular track of 500 m with speeds in the ratio

of 5:3, In how many distinct points would they meet, if they are start from a point

which is diametrically opposite to each other and in opposite direction ?

(1) 1 (2) 2 (3) 3 (4) 8

7. A and B run a 10 km race on a round course of 500 m. If their speeds are in

the ratio 3 : 2, then how many times will the winner of the race cross the other

participant?

(1) 2 (2) 6 (3) 9 (4) 12

8. Amol and Avash start running simultaneously around a circular track from the

same point in the same direction. Amol can complete 1 round in 15 seconds and

Avash can do the same in 25 seconds. Find the time after which they would be

together for the first time.

(1) 15 sec (2) 22.5 sec (3) 37.5 sec (4) 75 sec

9. Two persons start cycling simultaneously from a point P on a circular track. If they

travel at a speeds of 3 km/hr and 10 km/hr respectively, then what is the ratio of

number of distinct points that they would meet on that track then when they travel in

the same direction first to that when they travel in the opposite direction?

(1) 7 : 13

(2) 3 : 10

(3) 3 : 7

(4) 30 : 13

10. A race of 8000 m is conducted around a circular track having a track length

2000 m. The fastest and the slowest runner start the race in the same direction

from the same point and meet after 10 minutes. If the fastest runner has a speed

twice the slowest runner then what is the time taken by the slower runner to finish

the race?

(CAT-2003)

(1) 40mins (2) 35mins

(3) 20mins (4) 50 mins

CLOCKS

11. What is the angle between the hands of the clock at 6: 40 ?

12. When do the hands of the clock coincide between 6 and 7 ?

13. At what time is the angle between the hands of a clock 30o between 6 and 7 ?

14. A clock loses 15 min every hour. Another gains 30 minutes every hour.

If both of them are sync’ed at 12 noon on Tuesday, find

1) When will they both show the same time again ? What is the correct time

then ?

2) What is the correct time on Wednesday, if the faster clock shows

6 PM (on Wednesday) ?

15. Ram`s watch which gains time uniformly is 4 minutes slow at noon of Jan

1st and 38 minutes ahead exactly a fortnight later. When does the watch show

the correct time?

(1) Noon, Jan 2nd

(2) 4 pm, Jan 2nd

(3) 8 pm, Jan 2nd

(4) 4 pm, Jan 3rd

Thank You

arkss@careerlauncher.com