Question

Four bells toll together at 9:00a.m. They toll after 7,8,11 and 12 seconds respectively. How many times will they toll together again in the next three times?

Answer 1

Hint: According to the question, we need to find how many times it will happen that the bells ring together. We are provided with the information that after how many seconds the bells toll and from this using the concept of least common multiple we will be able to find the number that they toll together.

Complete step-by-step solution:
According to the question, we are given that all the four bells ring together at 9:00a.m. and after that we are given that they ring after 7, 8, 11 and 12 seconds.
Now, we need to find that in the next three tools of each bell how many times it happens that they ring together.
Now, from the given information we have that the LCM of 7, 8, 11, 12 is 1848 which means that the four bells tolls together after every 1848 seconds.
Now, we know that in three hours we have $3\times 3600=10800$ seconds.
Therefore, number of times the bell will toll
$\begin{align}
  & =\dfrac{10800}{1848} \\
 & \Rightarrow 5 \\
\end{align}$
Hence, we can say that the bell will ring 5 times in the next three hours.

Note: In such types of questions, we need to basically be very clear with the logic and also sharp at evaluating when we have time constraint. Now, for this we need to find the relation so that we can relate the tolls at different seconds at once so for that we need to be aware with the concept of highest common divisor and least common multiple which are mainly used in such situations when we need to find common things.