## Meeting someone on Circular Track..

No no….don’t get it wrong.

Here, we are talking about one of the interesting topics in CAT-preparation (and all others MBA entrance tests also) i.e. **Circular motion** – a small but very important part of a broader topic: Time, Speed and Distance.

We are specifically focusing here on the meetings of the runners on a circular track (or any *closed* track for that matter). As we go on, I will post some questions and in the explanation I’ll discuss few important concepts that’ll remain with you at the end of this session.

To get the best benefit, first solve the questions on your own before seeing the solutions.. 🙂

**When two runners run in SAME direction:**

**Problem 1.** Shyam and Shreya start running simultaneously from a point O on a circular track in same direction. If the ratio of their speeds is 7 : 4 respectively, then how many times do they meet each other till they reach O again?

(1) 2

(2) 3

(3) 4

(4) 7

**Problem 2.** Two persons, Ali and Baba, start running simultaneously from a point O on a circular track in the same direction. If the ratio of their speeds is 16 : 11 respectively, how many times are they diametrically opposite to each other before they meet at O for the next time?

(1) 3

(2) 4

(3) 5

(4) 6

(5) 7

**Problem 3.**Ali and Baba start simultaneously at the same point on a circular track and run along the track in the same direction. The point on the track at which they meet for the 29th time is same as that at which they meet for the 41st time. If the ratio of the speed of the faster boy to that of the slower one is n : 1 where n is a natural number. Which of the following is not a possible value of n?

(1) 2

(2) 4

(3) 5

(4) 6

**Problem 4.**Two motorcyclists, Angad and Bali, start simultaneously from a point S on a circular track and drive around the track in same direction with speeds of 9 km/hr and 5 km/hr respectively. Every time Angad overtakes Bali (anywhere on the track), both of them decrease their respective speeds by 1 km/hr. If the length of the track is 1 km, how many times do they meet at the starting point before Bali comes to rest?

(1) 0

(2) 1

(3) 2

(4) 4

**Problem 5.**How many times the angle between the minute hand and hour hand of a wall clock becomes 13-degree in a day?

(1) 13

(2) 22

(3) 26

(4) 44

**When two runners run in OPPOSITE direction:**

**Problem 6.** Anu and Vibhu start simultaneously from the same point on a circular track and run around the track in opposite directions. The radius of the track is 70m and the speeds of Anu and Vibhu are 20m/s and 10m/s respectively. Find the difference in distances travelled by Anu and Vibhu when both meet for the 9th time.

(1) 440m

(2) 880m

(3) 1320m

(4) 1760m

**Problem 7.**Arun and Barun start running simultaneously from same point on a circular track in opposite directions and with speeds in the ratio of 3 : 5 respectively. Every time they meet, they interchange their speeds and also reverse their directions. At how many distinct points on the track do they meet each other, if they run continuously?

(1) 2

(2) 3

(3) 5

(4) 8

**Problem 8.**Aalu and Bhalu start simultaneously from same point on a circular track, of length 4 km, and run in opposite directions. Their speeds are doubled every time they cross each other. Find the number of times they will meet within the first hour given that they started the race with respective speeds of 3 km/h and 5 km/h.

(1) 3

(2) 5

(3) 8

(4) Infinitely many

Huff!!! That’s all for the day. Enjoy!! 🙂

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