Question

Each of X alarms tolls at regular intervals. All of them toll together twelve times a day. No two alarms toll at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X?

Answer 1

Answer:

The alarm tolls together twelves times a day. Therefore, they toll together once every 2 hours (or 120 minutes). The number of factors =(3+1)×2×2=16. The maximum value of X is 16.

Answer 2

All the alarms strike together 12 times in a day .

$24 \div 12 = 2$

As there are 24 hrs in one day, they strike after every 2 hours.ie 120 minutes.

As the alarm strike at regular intervals and no two alarm strikes at the equal intervals ,finding the factors of 120 will give us the no of such alarms ie the maximum value of X.

There are total 16 Factors of 120 so the answer will be 16.

How to find the factors of a number-

Eg- We have to find the factors of 20 .

$1 \times 20$

All nos will have two factors- 1 and itself

Now we start with the smallest factors and write in the same format as written above.

$2 \times 10$

now we have two more factors 2 and 10.

10 will be the last factor as it divides the no into half, as we have already taken the no itself

$4 \times 5$

4 and 5 are other factors.

So the total number of factors for 20 are :-

$1,20,2,10,4,5$

Now for the given number in the question- 120

All nos will have minimum two factors so 1 and 120.

The other factors will be:-

$2×60, 3×40, 4×30 , 5×24, 6×20, 8×15 , 10×12$

So the total number of factors of 120 are 16

Further links-

https://www.google.com/url?sa=t&source=web&rct=j&url=https://brainly.in/question/17143849&ved=2ahUKEwijgujK7M_5AhV34TgGHX-dDIQQjjh6BAgMEAE&usg=AOvVaw0euNLtIt91Ac_r2iOVf8yn

https://www.google.com/url?sa=t&source=web&rct=j&url=https://brainly.in/question/3922252&ved=2ahUKEwjzsJTW7M_5AhXX1zgGHfKDCs4Qjjh6BAgLEAE&usg=AOvVaw39W0lySsJibzstEnwJbj2X

CODE #SPJ2