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 .
Answer & explanation
Correct answer: option 1
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