4 bells toll together at 9 a.m. They toll after 5 , 8 ,11 and 12 seconds respectively. How many times will they toll together again in the next 3 hours?
Answers
Answer:
Step-by-step explanation:
= 5.84 times that is 5 times.
LCM of 7s , 8s ,11s ,12 is : 7 * 2 *2*2 *11 * 3 = 1848 sec = 30 min and 48 seconds. so we add 30 m 48 sec to the previous time instant that they tolled together. next it will be at 12 h 04 min 48 sec.. this is after 3 hrs from 9 am.
HOPE IT HELPS YOU.
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 .