Question

A starts running at a speed of 10 km/hr from point X towards Y. At the same time B starts
running at a speed of 8 km/hr from point Y towards X. If the distance between X and Y is 350
meters then after how much time will they meet?​

Answer 1

Answer:

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CAT Races: Circular Races

Two friends A and B simultaneously start running around a circular track . They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

A. 3

B. 4

C. 7

D. 5

Step-by-step explanation:

CAT Races: Races in a square

Consider a square ABCD. EFGH is another square obtained by joining the midpoints of the sides of the square ABCD where E, F , G amd H are the midpoints of AB, BC, CD and DA respectively. Lakshman and Kanika start from points B and D respectively at speeds ‘l’ kmph and ‘k’ kmph respectively and travel towards each other along the sides of the square ABCD. Jagadeesh starts from Point E and travels along the Square EFGH in the anti-clockwise direction at ‘j’ kmph. Lakshman and Kanika meet for the second time at H where Jagadeesh also meets them for the first time. If l : k : j is 1: 3 : 5√2 then the distance travelled by Jagadeesh is

A. 7.5√2 times the side of the square ABCD

B. 7.5√2 times the side of the square EFGH

C. 7.5 times the side of the square ABCD

D. 7.5 times the side of the square EFGH

Understanding of relative speed would help.

Let track length be equal to T.

Time taken to meet for the first time = Trelativespeed = T6−b or Tb−6

Time taken for a lap for A = T6

Time taken for a lap for B = Tb

So, time taken to meet for the first time at the starting point = LCM (T6,Tb) = THCF(6,b)

Number of meeting points on the track = Time taken to meet at starting point/Time taken for first meeting = Relative speed / HCF (6,b).

So, in essence we have to find values for b such that 6−bHCF(6,b) = 2 or b−6HCF(6,b) = 2

The question is " If two people cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?"

b = 2, 10, 18 satisfy this equation. So, there are three different values that b can take.

Hence, the answer is 3.

Choice A is the correct answer.