175
Q:

A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?

 A) 48 min. past 12. B) 46 min. past 12. C) 45 min. past 12. D) 47 min. past 12.

Answer:   A) 48 min. past 12.

Explanation:

Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.

24 hours 10 min. of this clock = 24 hours of the correct clock.

$\inline \fn_jvn \frac{145}{6}$ hrs of this clock = 24 hours of the correct clock.

29 hours of this clock = $\inline \fn_jvn (24\times \frac{6}{145}\times 29)$ hrs of the correct clock

= 28 hrs 48 min of the correct clock.

Therefore, the correct time is 28 hrs 48 min. after 8 a.m.

This is 48 min. past 12.

Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.15 is

 A) 0 B) 37.5 C) 27 D) 15

Explanation:

Angle between hands of a clock

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

=> $\fn_jvn \small 30\left ( H -\frac{M}{5} \right )+\frac{M}{2}$ degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle

$\fn_jvn \small 30\left ( H -\frac{M}{5} \right )+\frac{M}{2}$ = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

8 776
Q:

What is the angle made by the hour hand and the minute hand, if the clock shows 9:15 pm ?

 A) 165 degrees B) 172.5 degrees C) 112.5 degrees D) 125.5 degrees

Explanation:

The minute hand angle is the easiest since an hour (i.e. 60 minutes) corresponds to the entire 360 degrees, each minute must correspond to 6 degrees. So just multiply the number of minutes in the time by 6 to get the number of degrees for the minute hand.
Here 15 minutes corresponds to 15 x 6 = 90 degrees

Next, you have to figure out the angle of the hour hand. Since there are 12 hours in the entire 360 degrees, each hour corresponds to 30 degrees. But unless the time is EXACTLY something o'clock, you have to write the time as a fractional number of hours rather than as hours and minutes.
Here the time is 9:15 which is (9 + 15/60) = 37/4 hours. Since each hour corresponds to 30 degrees, we multiply 30 to get (37/4)(30) = 277.5 degrees.

Since the hour hand is at 277.5 degrees and the minute hand is at 90 degrees, we can subtract to get the angle of separation. 277.5 - 90 = 187.5 =~ 360 - 187.5 = 172.5 degrees.

7 1322
Q:

How many minutes does a watch lose per day, if its hands coincide every 64 minutes ?

 A) 36 7/9 min B) 32 8/11 min C) 34 3/11 min D) 65 5/11 min

Explanation:

55 min. spaces are covered in 60 min.

60 min. spaces are covered in min. = min.

Loss in 64 min. = min.

Loss in 24 hrs = min. = min.

6 983
Q:

How many degrees will the minute hand move, in the same time in which the second hand move 4800 ?

 A) 80 deg B) 160 deg C) 140 deg D) 135 deg

Explanation:

As minute hand covers, 60 degrees

Minute hand covers 4800/60 = 80°

2 898
Q:

At what time, between 3 o’clock and 4 o’clock, both the hour hand and minute hand coincide each other  ?

 A) 3:16 7/11 B) 3:16 11/4 C) 3:30 D) 3:16 4/11

Explanation:

Coincide means 00  angle.

This can be calculated using the formulafor time A to B means  [11m/2 - 30 (A)]

Here m gives minutes after A the both hands coincides.

Here A = 3, B = 4

0 =11m/2 –30 × 3
11m = 90 × 2 = 180
m= 180/11 = 16 4/11

So time = 3 : 16 4/11