Question
Download Solution PDFThree runners Aman, Ramesh, and Naresh run a race, with Aman finishing 48 metres ahead of Ramesh and 68 metres ahead of Naresh. In another race of the same length, Ramesh finishes 25 meters ahead of Naresh. Each runner travels the entire distance at a constant speed. Find the length of the race.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Aman finished 48 metres ahead of Ramesh
Aman finished 68 metres ahead of Naresh
In another race of the same length, Ramesh finishes 25 meters ahead of Naresh.
Calculation:
Let the total distance of a race be D meters.
When Aman travels a distance of D meters, then Ramesh must have traveled (D - 48) meters.
Also, When Aman travels a distance of D meters, then Naresh must have traveled (D - 68) meters.
In another race of the same length, Ramesh finishes 25 meters ahead of Naresh.
When Ramesh travels a distance of D meters, then Narsh must have traveled (D - 25) meters.
Comparing both scenarios, of Ramesh and Naresh,
⇒ \({(D - 48)\over (D - 68)} = {D\over(D - 25)}\)
⇒ D2 - 73D + 1200 = D2 - 68D
⇒ 1200 = 5D
⇒ D = 1200/5 = 240
∴ The length of the race is 240 meters.
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