Three 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 metres ahead of Naresh. Each runner travels the entire distance at a constant speed. Find the length of the race.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 240 metres
Let the length of the race be x meters, which is finished by Aman
According to the question
⇒ Ramesh finishes (x - 48) m
⇒ Naresh finishes (x - 68) m when Aman covers x meters
Now, when Ramesh finishes x meters, Naresh finishes (x - 25) meters.
⇒ Aman/Ramesh = x/(x - 48)
⇒ Aman/Naresh = x/(x - 68)
⇒ Ramesh/Naresh = (x - 48)/(x - 68).........1
⇒ Ramesh/Naresh = x/(x - 25) ..............2
Solving equations 1 and 2
⇒ (x - 48)/(x - 68) = x/(x - 25)
⇒ (x - 48) × (x - 25) = x × (x - 68)
⇒ 73x - 68x = 1200
⇒ 5x = 1200
⇒ x = 1200/5 = 240 meters.