X and Y travel at distance of 90 km each such that the speed of Y is greater than the speed of X . The sum of their speeds is 100 km/h and the total time taken by both of them is 3 hours 45 minutes . Find the ratio of speed of X and Y .

2 : 3

Time = 3 hours  45 minutes = \(\frac{15}{4}\) hour

x + y  =  100  km/hr

ATQ,

\(\frac{90}{x}\) + \(\frac{90}{y}\) = \(\frac{15}{4}\)

\(\frac{6(x\;+\;y)}{xy}\) = \(\frac{1}{4}\) ⇒ \(\frac{6\;(100)}{xy}\) = \(\frac{1}{4}\)

⇒ xy = 2400, and also x + y = 100

On solving we get two factor i.e. 60 , 40 and it is mentioned that speed of Y is greater than the speed of X .  

So, X = 40  &  Y = 60

 X  :  Y = 40 : 60 = 2  :  3