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A and B start simultaneously from the same point along a circular track of length 1 km in the same direction at 4 m/sec and 5 m/sec respectively.
(i) When will they meet for the first time and at what point with respect to the starting
point in the direction of their sprint will they meet.
(ii) When will they meet for the first time at the starting-point?

A) (i) A has run 3 laps and B has run 4 laps (ii) 750 seconds
B) (i) A has run 4 laps and B has run 5 laps (ii)1000 seconds
C) (i) A has run 5 laps and B has run 6 laps (ii)1250 seconds
D) (i) A has run 5 laps and B has run 4 laps (ii)1500 seconds

Correct Answer:


B) (i) A has run 4 laps and B has run 5 laps (ii)1000 seconds

Description for Correct answer:
(i) A and B run in the same direction. Therefore, their relative speeds = 5 - 4 = 1 m/sec.

They will meet for the first time in \( \Large \frac{1000}{1} \)= 1000 seconds from the time they started the race.

In 1000 seconds, A would have run 4000 m and B would have run 5000 m. i.e., they both will be at the starting point. That is, they will meet after A has run 4 laps and B has run 5 laps.

(ii) A will take \( \Large \frac{1000}{4} \) = 250 seconds to complete one round along the track.

B will take \( \Large \frac{1000}{5} \) = 200 seconds to complete one round along the track.

The L.C.M. of 2000 and 250 = 1000 seconds. They will meet for the first time at the starting point after 1000 seconds.

Part of solved Time and Distance questions and answers : >> Aptitude >> Time and Distance

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Similar Questions

1). A and B start on a circular track of length 400 m simultaneously from the same point in
opposite direction running at 5 m/sec and 3 m/sec respectively.
(i) When will they meet for the first time?
(ii) What point with respect to the starting point in the direction in which A runs will they meet?
(iii) When will they meet for the first time at the starting point?
(iv) How many times would they have met before they meet for the first time at the starting
point again?

A). (i) 60 seconds (ii) 350 m (iii) 450 seconds (iv) 6 times

B). (i) 40 seconds (ii) 200 m (iii) 350 seconds (iv) 8 times

C). (i) 50 seconds (ii) 250 m (iii) 400 seconds (iv) 7 times

D). (i) 80 seconds (ii) 300 m (iii) 500 seconds (iv) 5 times

2). A and B run around a circular track of radius 70 meters starting from the same point simultaneously and in the same direction. lf A runs at 25 m/min and B runs at 36 m/min, when will they meet for the first time?

A). 50 min

B). 55 min

C). 60 min

D). 40 min

3). Three people A, B and C run around a circular track of length 400 m starting simultaneously from the same point in the same direction at 5m/sec, 8 m/sec and 3 m/sec respectively.
(i) When will they meet for the first time and at what point will they meet?
(ii) When will they meet for the first time at the starting point?

A). (i) 400 seconds (ii) 400 seconds

B). (i) 450 seconds (ii) 500 seconds

C). (i) 500 seconds (ii) 550 seconds

D). (i) 300 seconds (ii) 400 seconds

4). In a kilometer race, A beats B by 10 seconds or 60 meters. How long does B take to run the course?

A). 166.67 Secs,

B). 233.33 Secs.

C). 333.67 Secs.

D). 266.67 Secs.

5). A runs \( \Large 2\frac{1}{4} \) times as fast as B. In a race between A and B, A wins by 75 meters. What is the length of the race?

A). 100 meters

B). 135 meters

C). 150 meters

D). 200 meters

6). A can run half a kilometer in1 min 30 seconds. B can run the same distance in 1 min 40 sec. In a kilometer race between A and B, by how many meters will A win the race?

A). 120 meters

B). 75 meters

C). 100 meters

D). 110 meters

7). P and Q run a kilometer and P wins by 30 seconds. P and R run a kilometer, and P wins by 250 meters. Q and R run a kilometer and Q wins by 30 seconds. Find the time taken by P, Q and R to run a kilometer.

A). P-155 sec., Q-185 sec, and R-215 sec.

B). P-160 sec., Q-190 sec, and R-220 sec.

C). P-190 sec., Q-220 sec, and R-250 sec.

D). P-180 sec., Q-210 sec, and R-240 sec.

8). A takes 4 minutes 50 seconds while B takes 5 minutes to complete the race. If they start the race simultaneously from the same point, then A beats B by \( \Large 66\frac{2}{3} \) meters. Find the length of the race.

A). 2000 meters

B). 2200 meters

C). 1000 meters

D). 1500 meters

9). A can run 100 meters in 13 seconds, and B takes 15 seconds to complete the same 100 meters. lf A and B run a 100 m race, by how many meters will A win the race?

A). 16.67 meters

B). 13.33 meters

C). 21.33 meters

D). 15.67 meters

10). lf A and B run a kilometer, A is allowed to start 330 meters ahead of B. If the ratio of the speeds of A and B is 2 : 3, who wins the race and by what distance?

A). B wins by 5.50 meters

B). B wins by 6.67 meters

C). B wins by 3.33 meters

D). B wins by 4.67 meters