Question : Three persons P, Q, and R run along a circular track at speeds of 3 km/hr, 4 km/hr, and 6 km/hr respectively. If the length of the track is 36 km, then how much time will they meet again at the starting point?
Option 1: 38 hours
Option 2: 36 hours
Option 3: 24 hours
Option 4: 28 hours
Correct Answer: 36 hours
Solution :
Speed = $\frac{\text{Distance}}{{\text{Time}}}$
The time it takes for each person to run one lap is:
For P:
$T_P = \frac{36}{3} = 12 \text{ hours}$
For Q:
$T_Q = \frac{36}{4} = 9 \text{ hours}$
For R:
$T_R = \frac{36}{6} = 6 \text{ hours}$
The time at which they all meet again at the starting point is the least common multiple (LCM) of $T_P$, $T_Q$, and $T_R$.
The LCM of 12, 9, and 6 hours is 36 hours.
Hence, the correct answer is 36 hours.
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