At a certain time I looked at a 24 hour digital clock and noticed some things about the time:

1)The number in the hours section plus the number in the minutes section makes 60.

2)One of the digits in the minutes section is the square root of the other digit in the minutes section.

3)The sum of the digits in the minutes section is the number in the hours section reversed.
What was the time?

(In reply to

answer by K Sengupta)

Since none of the digits in the decimal number system can exceed 9 and the number in the minutes section (mm) is <=59, it follows that the possible values of mm in conformity with condition (ii) are:

00, 11, 24, 42 and 39.

Since the number in the hours section (hh) is <=23, in terms of condition (i), the first two mm values are invalidated, so that we must have:

hh:mm = 36:24, 18:42, 21:39

The first two values violate condition (iii). However, the third value satisfies condition (iii), since 21 is the reversal of 3+9 = 12.

Consequently, the required time is 21:39

*Edited on ***April 11, 2008, 3:48 am**