@ Test Group 1
Choose the correct option.
Awatch manufacturing company is testing watch alarms. They program alarms of all the
watches to beep simultaneously. The alarms start beeping at intervals of 5. 8. 10. 15 and
21 seconds respectively. In an hour, how many times do the alarms beep together?
Answers
Given :- A watch manufacturing company is testing watch alarms. They program alarms of all the watches to beep simultaneously. The alarms start beeping at intervals of 5 ,8, 10, 15 and 21 seconds respectively. In an hour, how many times do the alarms beep together ?
Solution :-
As we know all the alarms beeps first time together will be the time after LCM of their beeping time alone .
So, we have to find LCM of (5, 8, 10, 15 and 21).
Prime factors of 5, 8, 10 , 15 and 21 :-
→ 5 = 1 * 5
→ 8 = 2 * 2 * 2
→ 10 = 2 * 5
→ 15 = 3 * 5
→ 21 = 3 * 7
LCM = 2 * 2 * 2 * 3 * 5 * 7 = 840 seconds.
now, we know that,
→ 60 seconds = 1 minute .
→ 1 second = (1/60) minute .
→ 840 seconds = (1/60) * 840 = 14 minutes.
Therefore, we can conclude that, all the alarms beeps together first time after 14 minutes.
now, we know that,
→ 60 minutes = 1 hour.
So,
→ in 14 minutes alarms beeps = first time .
→ in 28 minutes alarms beeps = second time.
→ in 42 minutes alarms beeps = third time.
→ in 56 minutes alarms beeps = fourth time.
Hence, In an hour, the alarms beep together for 4 times .
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