Question

Four bells toll together at 9 am . they toll after 7,8,11 and 12 seconds respectively. how many times will they toll again in the next 3 hours ?

Answer 1

Answer:

5

Step-by-step explanation:

Answer 2

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 .