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:

Answer: Option B

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