Question

In a school, the duration of a period in the junior section is 40 minutes and the senior section is 1 hour. If the first bell for each section rings at 9:00 am, when will the two bells ring together again?

Answer 1

Hint: First find the time when the first bell rings and when the other ring bells in both the sections, after that find the time which is the common time for both the sections.

Complete answer:
It is given in the problem that the duration of a period in the junior section is 40 minutes and the senior section is 1 hour that is minutes and it is also given that the first bell for each section rings at 9:00 am.
The goal of the problem is to find that when will the two bells ring together again.
The time duration of the period of junior section min
The time duration of the period of senior section min
Now, take a look on the table that gives the time when the other bells ring in both the sections:

Number of periods	1	2	3	4	5	6	7
Junior section	40	80	120	160	200	240	280
Senior section	60	120	180	240	300	360	420

It can be seen from the above table that the third period of the junior section rang after the \[120\] minutes of the first bell and the second period of the senior section also rang after the $120$ minutes of the first period. It means that the two bells ring together after the $120$ minutes, and this bell is the third bell of the junior section and second bell of the senior section. The first bell for each section rings at \[9:00\]am.
$120$ minutes is also given as $2$ hours. Then the time when the bell rings together after the first bell ring is:
$9:00$am$ + 2$hours$ = 11:00$am.

Therefore, the two bells rings together again at $11:00$am.

Note: We can also solve this problem by finding the least common multiple of both the times $40$ and $60$. Find the least common multiple of both the numbers using the method of factorization method.

2	40,60
2	20,30
2	10,15
2	5,15
3	5,5
5	1,1

Then, the LCM of the numbers $40$ and $60$ is:
LCM$ = 2 \times 2 \times 2 \times 3 \times 5$
LCM$ = 120$
$120$ minutes is also given as $2$ hours. Then the time when the bell rings together after the first bell ring is:
$9:00$am$ + 2$hours$ = 11:00$am.

Therefore, the two bells rings together again at $11:00$am.