There is a point P on the circle. A and B started running in two constant different speeds. A in Clockwise and B in Anti-clockwise. First time 500 m in Clockwise from P then 400 Anti-clockwise. If B is yet to complete one round, What is the circumference of the circle? Choose the most appropriate option: A) 700 B) 800 C) 900 D) 1000 E) 1100

Rationale: let the speeds of a & b be u and v resp . and let circumference be c . let their first meeting be after time t then ut + vt = c and ut = 500 ∴ vt = c − 500 and u / v = 500 / ( c − 500 ) for their second meeting after time t , ut + vt = 2 c and vt = 400 ∴ ut = 2 c − 400 and u / v = ( 2 c − 400 ) / 400 hence 500 / ( c − 500 ) = ( 2 c − 400 ) / 400 simplifying , 100000 = ( c − 200 ) ( c − 500 ) = c ² − 700 c + 100000 → c = 700 answer : a
Answer: A