Question

Suppose you have a 12-hour digital clock
where the number representing the hour is
always the same as the number representing
the minute. That is, the clock can only show
times like 8:08, 9:09, 10:10, etc. What is the
smallest time difference between two such
times ?
(1) 101 minutes
(2) 61 minutes
(3) 60 minutes
(4) 49 minutes​

Answer 1

Answer

Smallest difference is between 12:12 and 1:01 which is 49 minutes.

Hence Option (4) is correct

Answer 2

The right option for this question is option 4: 49 minutes​

Given:

12-hour digital clock

The digital clock shows timing as:

1:01

2:02

3:03

4:04

5:05

6:06

7:07

8:08

9:09

10:10

11:11

12:12

To find:

Smallest difference between the two such times=?

Solution:

The find the smallest difference between time interval we need to calculate difference between all time intervals.

=> Difference between 1:01 and 2:02

= 60 minutes + 1 minute = 61 minutes

=> Difference between 2:02 and 3:03

= 60 minutes + 1 minute = 61 minutes

=> Difference between 3:03 and 4:04

= 60 minutes + 1 minute = 61 minutes

=> Difference between 4:04 and 5:05

= 60 minutes + 1 minute = 61 minutes

=> Difference between 5:05 and 6:06

= 60 minutes + 1 minute = 61 minutes

=> Difference between 6:06 and 7:07

= 60 minutes + 1 minute = 61 minutes

=> Difference between 7:07 and 8:08

= 60 minutes + 1 minute = 61 minutes

=> Difference between 8:08 and 9:09

= 60 minutes + 1 minute = 61 minutes

=> Difference between 9:09 and 10:10

= 60 minutes + 1 minute = 61 minutes

=> Difference between 10:10 and 11:11

= 60 minutes + 1 minute = 61 minutes

=> Difference between 11:11 and 12:12

= 60 minutes + 1 minute = 61 minutes

=> Difference between 12:12 and 1:01

= 12:12 to 1:12 = 60 minutes

= 12 minutes - 1 minute = 11 minutes

= 60 minutes = 11 minutes

= 49 minutes

Hence, 49 minutes is the smallest difference between two such times that is 12:12 and 1:10.