4 bells toll together at 9:00 am. they toll after 7, 8, 11 and 12 seconds respectively. how many times will they toll together again in the next three hours?
Answers
After every 1848 secs they will toll together. In 3 hours there are 10800 secs .. so they will toll together 5 times in the next 3 hours .
Answer:
Step-by-step explanation:
Gɪᴠᴇɴ :-
Four bells toll together at 9:00AM.
They toll after 7,8,11,12 seconds respectively..
Tᴏ Fɪɴᴅ :-
How many times will they toll together again in the next 3 hours ?
ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-
If some bells toll After a,b,c,d Seconds , Than, They will toll together again after LCM of (a,b,c,d).
1 Minute = 60 Seconds .
Sᴏʟᴜᴛɪᴏɴ :-
Four Bells toll together at 9:00AM. .
Than, After 9AM first Time They will bell After :- LCM of (7,8,11,12)
Prime Factorization :-
→ 7 = 1 * 7
→ 8 = 2*2*2 = 2³
→ 11 = 1 * 11
→ 12 = 2 * 2 * 3 = 2² * 3
→ LCM = 7 * 8 * 11 * 3 = 1848 Seconds. = (1848/60) = 30 Min + 48 Seconds .
Hence, After 9AM all 4 Bells toll after 30 Min + 48 Seconds . .
_________________
Now, in Next 3 Hours They will Toll :-
→ 3 Hours = 3 * 60 = 180 Minutes.
→ 30 Min + 48 Seconds = 30 (48/60) = 30(4/5) = (154/5) Min.
So,
→ In (154/5) Min. Bells Toll = 1 Time
→ in 1 Min. Bells Toll = (1) / (154/5) = (5/154) Time.
→ in 180 Min. Bells Toll = (5/154) * 180 = 5 Times.
Therefore, They toll together again 5 Times in the next 3 hours .