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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

Correct Answer:



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

Description for Correct answer:
(i) Since A and B run in opposite directions, their relative speed = 5 + 3 = 8 m/sec.

They will meet for the first time in \( \Large \frac{400}{8} \) = 50 seconds.

(ii) In 50 seconds, A would have covered a distance of \( \Large 50 \times 5 \) = 250 m from the starting point in his direction.

(iii) A will take \( \Large \frac{400}{8} \) = 80 seconds to complete one lap along the circular track.

B will take \( \Large \frac{400}{3} \) seconds to complete one lap along the circular track.

L.C.M of 80 and \( \Large \frac{400}{3} \) is 400 seconds. Therefore, A and B will meet for the first time at the starting point in 400 seconds.

(iv) As they meet each other every 50 seconds, they will meet for the first time at the starting point at the 8th time from the time they start the race and will meet once at the starting point for every 8 times they meet. i.e., they would have met 7 times before they meet at the starting point for the first time.

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

Comments

Similar Questions

1). 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

2). 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

3). 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.

4). 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

5). 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

6). 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.

7). 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

8). 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

9). 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

10). A takes 20 seconds lesser to run a kilometer than B does. Even if A allows B to start 125 meters ahead in the race, A will win by 125 meters. How long will A and B take to complete the course?

A). A - 50 seconds, B - 70 seconds

B). A - 70 seconds, B - 90 seconds

C). A - 80 seconds, B - 100 seconds

D). A - 60 seconds, B - 80 seconds