Q1. Modulo Arithmetic

There are 24 hours in a day. To know the time we use clocks. There are mainly two types of clocks. 12 hours clock and 24 hours clock. 12 hours clock repeat itself twice in a day i.e. 24 hours of a day are divided into two periods called a.m. (ante meridiem) and p.m. (post meridiem). Each period consists of 12 hours numbered 12 (acting as 0), 1, 2, 3, 4, 5, 6,7,8,9, 10, 11. Then 24 hours per day cycle starts at 12 midnight (usually indicated as 12 a.m.) runs through 12 noon (usually indicated as 12 p.m.) and continues just before midnight at the end of the day.



Based on the above information, answer the following questions:

(i) It is currently 7:00a.m. in 12 hours clock. The time in next 492 hours will be

(a) 7:00a.m.
(b) 7:00 p.m
(c) 19:00a.m.
(d) 19:00 p.m.

(ii) If the time after 640 hours from now will be 9:00 p.m., then current time is

(a) 5:00a.m.
(b) 5:00 p.m.
(c) 4:00 a.m.
(d) 4:00 p.m

(iii) What time in 24 hours clock is equivalent to 2:00 p.m. in 12 hours clock?

(a) 2:00
(b) 22:00
(c) 14:00
(d) 16:00

(iv) What time in 12 hours clock is equivalent to 20:00 in 24 hours clock?

(a) 4:00 a.m.
(b) 4:00 p.m.
(c) 8:00a.m.
(d) 8:00 p.m.

(v) Which of two times are same in 12 hours and 24 hours clocks respectively?

(a) 01:00a.m., 13:00
(b) 02:00 p.m., 02:00
(c) 03:00 p.m., 15:00
(d) 04:00a.m., 16:00

Solution