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

Solution (By Examveda Team)

Y's speed greater than X's speed.
Y > X
X + Y = 100 km/hr . . . . . . (i)
$$\eqalign{ & {\text{Total time}} = 3{\text{ hr }}45{\text{ min}} = 3\frac{{45}}{{60}} = \frac{{15}}{4}{\text{ hr}} \cr & {\text{Distance}} = \frac{{{S_1} \times {S_2}}}{{{S_1} + {S_2}}} \times {\text{Total time}} \cr & 90 = \frac{{X \times Y}}{{X + Y}} \times \frac{{15}}{4} \cr & X + Y = \frac{{90 \times 100 \times 4}}{{15}} \cr & X + Y = 2400{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr} $$
Solve equation (i) and (ii)
X = 40; Y = 60     [Y > X]
Ratio of X's speed and Y's speed = 40 : 60 = 2 : 3