Question

The first bell rings every $20$ minutes, second bell rings every $30$ minutes, and the third bell rings every $50$ minutes. If all three bells ring at the same time at $12:00pm$, when will the next time the three bells ring together?

Answer 1

Hint: In the given question, we are given that the first bell rings every $20$ minutes, second bell rings every $30$ minutes, and the third bell rings every $50$ minutes and we need to find when will be the next time three bells will ring together, if all three bells ring the same time at $12:00pm$. To solve this question, we will use the concept of LCM (LCM or the least common multiple is defined as the smallest positive number that is a multiple of two or more numbers). We will find the LCM of the three given bells ringing time that will give us the exact time on which all of them will ring again.

Complete step by step answer:
We are given that the first bell rings every $20$ minutes, the second bell rings every $30$ minutes and lastly, the third bell rings every $50$ minutes. We are also given that they ring together all at $12:00pm$.
Let us find the LCM of our given three numbers. Our given numbers are $20$, $30$ and $50$. The LCM of $20$, $30$ and $50$ will give us the exact time duration after which all the three bells will ring again.
So, the LCM of $20$, $30$ and $50$ = $10 \times 2 \times 3 \times 5$
$ = 300$
Hence, they will ring again after $300$ minutes. Now we have $300$ minutes = $5$ hours.
Therefore, they will ring again after $5$ hours, i.e. $12:00 + 5$ hours = $5:00$ pm. Hence, all three bells will ring together again at $5:00$ pm.

Note:
To convert minutes into hours, we have used the conversion formula as $1hour = 60 \text{minutes}$.
$ \Rightarrow 60 \text{minutes} = 1hour$
$ \Rightarrow 1 \text{minute} = \dfrac{1}{{60}} \, hour$
$ \Rightarrow 300 \text{minutes} = \dfrac{1}{{60}} \times 300\, hours = 5\,hours$
Students should be careful about the units. Calculation should be done in the same units.