Bunuel
Ronaldo and Messi race each other in an x-meter race. They start simultaneously from the same point. If Ronaldo, running at a content rate, covers the distance in 8 seconds, while Messi, running at a content rate, covers the distance in 10 seconds, in how many seconds the distance left to cover by Ronaldo is half the distance left to cover by Messi ?
A. 3 seconds
B. 10/3 seconds
C. 5 seconds
D. 20/3 seconds
E. Cannot be determined
An interesting question. We will solve it using ratios as we usually do. In races, we love to make diagrams.
Time taken R : M = 8 : 10
Speed R : M = 10 : 8 = 5 : 4 (speed is inverse of time taken)
Attachment:
Screenshot 2022-07-19 at 7.13.57 PM.png [ 16.64 KiB | Viewed 1875 times ]
So at any given time, if they start together, the ratio of their distances covered will be 5:4 (the ratio of their speeds). The difference between distances covered by them will be 1 unit on the ratio scale. Since the leftover distance of M should be twice the leftover distance of R, 1 unit of distance should be remaining for R (as we can see in the diagram)
So R would have covered 5/6th of the total distance in this time.
To cover complete distance of
x, R takes 8 secs.
To cover 5/6th the distance, R will take 8 * 5/6 = 20/3 secs
Answer (D)