Three bells P, Q and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes. If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time? A. 5:00 PM B. 5:30 PM C. 6:00 PM D. 6:30 PM

GATE 2022 · General Aptitude · LCM HCF · medium

Answer: All three bells ring together again at 5:00 PM, which is option A.

1. Prime factorize each interval: 20 = 2^2 x 5 | 30 = 2 x 3 x 5 | 50 = 2 x 5^2. Primes involved: 2, 3, 5. Max powers: 2^2 = 4, 3^1 = 3, 5^2 = 25.
2. Compute LCM(20, 30, 50): LCM = 2^2 x 3 x 5^2 = 4 x 3 x 25 = 300 minutes.
3. Convert 300 minutes to hours and find the clock time: 300 / 60 = 5 hours. Starting from 12:00 PM, adding 5 hours gives 5:00 PM.