Three bells ring at intervals of 12, 15 and 21 minutes. If they ring simultaneously at 9am, then next they will ring together at :
a.3 pm
b.6 pm
c.4 pm
d.12 pm
Answers
The next three bells will ring together at 4 pm
Given :
Three bells ring at intervals of 12, 15 and 21 minutes. If they ring simultaneously at 9 am
To find :
The time when next three bells will ring together at
a. 3 pm
b. 6 pm
c. 4 pm
d. 12 pm
Solution :
Step 1 of 2 :
Write down the given data
Here it is given that three bells ring at intervals of 12, 15 and 21 minutes. If they ring simultaneously at 9 am
Step 2 of 2 :
Calculate the time when next three bells will ring together
12 = 2 × 2 × 3
15 = 3 × 5
21 = 3 × 7
∴ LCM of 12 , 15 and 21
= 2 × 2 × 3 × 5 × 7
= 420
Now , 420 minutes = 7 hours
So after 7 hours three bells will ring again together
Since three bells ring simultaneously at 9 am
∴ The time when next three bells will ring together is 7 hours after 9 am i.e at 4 pm
Hence the correct option is c. 4 pm
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GIVEN:-
Three bells ring at intervals of 12, 15 and 21 minutes.
If they ring simultaneously at 9 am.
TO FIND:-
Next they will ring together at
SOLUTION:-
As per given question,
the bells ring at intervals of 12, 15 and 21 minutes .
∵the all bells ring simultaneously after X minutes.
X = L.C.M of 12, 15 and 21.
∴ 12 = 2 × 2 × 3
15 = 3 × 5
21 = 3 × 7
_____________
L.C.M = 2 × 2 × 3 × 5 × 7.
= 420
So, the bell will ring simultaneously after 420 minutes .
The time in hours = 420 / 60
= 7 hours .
∴ 9 am + 7 hours = 4 pm
Therefore, the correct option is (C) 4 pm.
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