Question

Discrete Mathematics! I need the right answer and the correct explanation. So I can learn this.

1. If a 12-hour clock currently reads 1 o'clock, what time will it read in 180 hours?

2. If a 24-hour clock currently reads 8 o'clock, what time will it read in 239 hours?

Answer 1

To solve this kind of Problems we use division Algorithm(means finding the Quotient and remainder of a Division)

Let us consider a N-hour's Clock which has Initial time Reading be X .And the reading of the clock after M Hours,

Using Division Algorithm M = (Quotient)*N +Remainder

Here Quotient represent the Number of rotations

Remainder represent the Number of hours the time ahead the Initial reading of the Clock

N is the format hours of the Clock

Time after M Hours will be (X+Remainder)%N where X is Initial time and N is Clock format

1)

Given The initial time of the clock is 1 o'clock then x = 1 o'clock

And the Clock format is 12 Hours then N is 12

We have to find the time will it read in 180 hours then M =180

180 = (15 x 12)+ 0 (Division rule)

Quotient is 15

Remainder is 0

Time reading after 180 hours is (1+0)%12 = 1 o'clock (according to (X+Remainder)%N)

Time will it read in 180 hours is 1'clock

2)

Given The initial time of the clock is 8'o'clock then x = 8 o'clock

And the Clock format is 24 Hours then N is 24

We have to find the time will it read in 239 hours then M = 239

239 = (9 x 24 )+23 (Division rule)

Quotient is 9

Remainder is 23

Time reading after 239 hours is (8+23)%24 (according to (X+Remainder)%N)

= 31%24  

= 7 o'clock

Time will it read in 239 hours is 7 o'clock

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