Question

In a call centre at New Delhi, it is observed that it gets a call at an interval of every 10 minutes from California, at an interval of every 12 minutes from Texas, at an interval of 20 minutes from Washington DC and after 25 minutes it gets a call from London. If in the early morning at 5:00 a.m. it has received the calls simultaneously from all the four destinations, then at which time again it will receive the calls at a time from all the places on the same day?
(a) 10:00 a.m.
(b) 3:00 a.m.
(c) 5:00 p.m.
(d) Both A and B

Answer 1

Hint: In this question we first need to find the least common multiple of 10, 12, 20, 25 so that we get the least number which is common to all those 4 numbers. Now, from the L.C.M we get the number of minutes after which they have a simultaneous call. Then add this time to the given time 5:00 a.m. to get the result.

Complete step-by-step answer:
Now, the given times in the question are 10 minutes,12 minutes, 20, minutes, 25 minutes
Let us now find the L.C.M of the above mentioned minutes
\[\Rightarrow L.C.M\left( 10,12,20,25 \right)=5\times 2\times 2\times 3\times 5\]
Now, on further simplification we get,
\[\therefore L.C.M\left( 10,12,20,25 \right)=300\]
Thus, for every 300 minutes the call centre will receive calls from all the mentioned places simultaneously
Let us now convert this minutes to hours for further simplification
As we already know that 60 minutes is equal to 1 hour now we get,
\[\Rightarrow 300\text{ minutes}=\dfrac{300}{60}\text{ hours}\]
Now, on further simplification we get,
\[\Rightarrow 300\text{ minutes}=5\text{ hours}\]
Let us now add this to the given time in the question
\[\Rightarrow 5:00\text{ a}\text{.m}+5\text{ hours}\]
Now, on simplifying this further we get,
\[\Rightarrow \text{10:00 a}\text{.m}\]
Hence, the correct option is (a).

Note: Instead of using the L.C.M we can also solve it by considering the A.P series to be formed by each of them and then consider the \[{{\text{n}}^{th}}\]term to be same and find its value. This method is a bit confusing and lengthier to solve.
It is important to note that there can be other possibilities for every 300 minutes. So, we need to check all the options whether they satisfy the given condition or not and then choose the answer.