Question

Calculate the next time and mention it using a.m. or p.m.
(i) 20 minutes after 6:05 p.m. =
(ii) 5 minutes after 2:10 a.m.=
(iii) 40 minutes after 10:30 a.m. =
(iv) 15 minutes after 12 midnight=
(v) 45 minutes after 4:30 p.m. =
(vi) 30 minutes after 7:35 a.m.=

Answer 1

Hint: Here we will use the clock and the rotation of the minute hand and the hour hand and a 12-hour time system to calculate the time as per requirement of the question.

Complete step by step solution:
Now in one day we have 12 hours of daylight and 12hours of darkness, and any time during the day is denoted with the suffix a.m., while any time in the rest of the day is denoted by p.m. in the suffix.
So, depending on the time on the clock as per the question we will calculate the next time in a.m. or p.m.

Now,
(i) 20 minutes after 6:05pm = 20 minutes later than 6:05p.m, which means the time will be in p.m. only and just 20 minutes will be added to the time in the minutes’ part.
The minute hand is already at 5 minutes past 6 at 6:05 p.m., so after 20 minutes the minute hand would have completed 20 more rotations and reached the 25 minutes marks, that is $05 minutes + 20 minutes = 25 minutes$

That is, at 20 minutes after 6:05 pm, the minute hand will now be at 25minutes past 6 while the hour hand will be at 6 and the time will be 6:25 p.m.

(ii) 5 minutes after 2:10 a.m.= 5 minutes later than 2:10 a.m., which means the time will be in a.m. only and just 5 minutes will be added to the time in the minutes’ part.
The minute hand is already at 10 minutes past 2 at 2:10 a.m., so after 5 minutes the minute hand would have completed 5 more rotations and reached the 15 minutes mark, that is $10 minutes + 5 minutes = 15 minutes$

That is, the minute hand will now be at 15minutes past 2 while the hour hand will be at 2 and the time will be 2:15 a.m.

(iii) 40 minutes after 10:30 a.m. = 40 minutes later than 10:30 a.m., which means the time will be in a.m. only and just 40 minutes will be added to the time in the minutes’ part.
The minute hand is already at 30 minutes past 10 in the morning at 10:30 a.m., so after 40 minutes the minute hand would have completed 40 more rotations and reached the 10 minutes’ mark of the next hour after 10 a.m.
that is $30 minutes + 40 minutes = 70 minutes$
Now, 70 minutes after 10 a.m. means 1 hour and 10 minutes after 10 a.m.
Which means the minute hand will be at 10 minutes past 11 a.m.

That is, at 40 minutes after 10:30 a.m. the minute hand will now be at 10 minutes past 11 while the hour hand will be at 11 and the time will be 11:10 a.m.

(iv) 15 minutes after 12 midnight = 15 minutes later than 12 midnight, now conventionally 12 at midnight is when the day time starts so all times after 12 midnight and till the next 11:59 in the morning will be in a.m., which means the time will be in a.m. only and just 15 minutes will be added to the time in the minutes’ part.
The minute hand and the hour hand both are at 12 midnight., after 15 minutes the minute hand would have completed 15 more rotations and reached the 15 minutes mark, that is $0 minutes + 15 minutes = 15 minutes$ after 12.

That is, at 15 minutes after 12 midnight, the minute hand will now be at 15minutes past 12 while the hour hand will be at 12 and the time will be 12:15 a.m.

(v) 45 minutes after 4:30 p.m. = 45 minutes later than 4:30p.m, which means the time will be in p.m. only and just 45 minutes will be added to the time in the minutes’ part.
The minute hand is already at 30 minutes past 4 at 4:30 p.m., so after 45 minutes the minute hand would have completed 45 more rotations and reached the 45 minutes marks, that is $30 minutes + 45 minutes = 75 minutes$ after 4 p.m. which means the minute hand would have completed 75 minutes now, 75 minutes means 1 hour and 15 minutes so that means the minute hand will now be at 15 minutes past the next hour after 4 p.m., which is 5 p.m.

That is, at 45 minutes after 4:30 p.m. the minute hand will now be at 15minutes past 5 while the hour hand will be at 5 and the time will be 5:15 p.m.

(vi) 30 minutes after 7:35 a.m.= 30 minutes later than 7:35 p.m., which means $30 minutes + 35 minutes = 65 minutes$ after 7 a.m.
$ \Rightarrow $ 65 minutes means 1 hour and 5 minutes after 7 a.m.
$ \Rightarrow $1 hour and 5 minutes after 7 a.m. will be 5 minutes past 8 a.m.
$ \Rightarrow $the time will be 8:05 a.m.

Note: While calculating the next times, the a.m. or p.m. of previous times have to be taken into consideration. Care has to be taken with the 12 at midnight and at noon when the time changes from a.m. to p.m. or vice-versa.