Question
Download Solution PDFTwo runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction.
Formula used:
When two runners run on a circular track of length D m at a m/sec and b m/sec, respectively, in the same direction.
Time taken by them to meet for the first time at starting point on the track
⇒ LCM (D/a , D/b)
Calculation:
The speed of Sony (S1) = 18 km/hr
⇒ 18 x (5/18) = 5 m/sec
The speed of Mony (S2) = 24 km/hr
⇒ 24 x (5/18) = 20/3 m/sec
Time taken by them to meet for the first time at the starting point on track
⇒ LCM (D/a , D/b)
⇒ LCM (200/5, 200/(20/3))
⇒ LCM (40, 30)
40 = 2 x 2 x 2 x 5
30 = 2 x 3 x 5
⇒ LCM (40, 30) = 2 x 2 x 2 x 3 x 5 = 120 seconds
∴ The required time is 120 seconds.
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