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/h and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2 : 3.
Let the speed of X and Y be 'a' and 'b' km/hr where b > a.
a + b = 100 km/hr.
90/b + 90/a = 15/4
[90(a + b)]/ab = 15/4
(90 × 100)/ab = 15/4
a2 - 100a + 2400 = 0
(a - 60)(a - 40) = 0
a = 60 , 40.
If a = 60 then b = 40 which is not possible.
If a = 40 then b = 60.
Ratio of speed of X and Y = a : b = 40 : 60 = 2 : 3.