a goes to place x and b goes to place y.
after a travelled 180 km more than b they together meet at a point between xy. they together had their lunch for half an hour. after that a took 2 hrs to reach x and b took 4.5 hrs to reach y. find distance between x and y?  Choose the correct choice from the following answers:	A) 900 km	B) 540 km	C) 720 km	D) 820 km	E) 920 km

Rationale: let speed of a be - - - - - - - sa let speed of b be - - - - - - - - sb let the distance covered by b while going to position xy be - - - - - - - - - - - x so distance covered by a in same time while going to xy is - - - - - - - - - - 180 + x ( it ' s given in the question ) so total distance b / w x and y is = x + ( x + 180 ) while going to position xy : - time taken by a = time taken by b ( x + 180 ) / sa = x / sb sa / sb = ( x + 180 ) / x - - - - - - - - - - - - - - - - - - - - - 1 after lunch : - a . c . t ( according to question ) sa = x / 2 sb = ( x + 180 ) / 4.5 dividing sa / sb = ( x * 4.5 ) / ( ( x + 180 ) * 2 ) - - - - - - - - - - - - - - - - - - - - 2 equating equations 1 and 2 9 / 4 = ( x + 180 ) ^ 2 / x ^ 2 now taking square root on both sides we get 3 / 2 = ( x + 180 ) / x x = 360 therefore distance between x and y = x + ( x + 180 ) = 900 km answer : a
Answer: A