Question 1

What is the ratio of 18 minutes to one hour ?

Accepted Answer

One hour = 60 min 18/60 = 3/10

Question 2

An accurate clock shows 7 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 3 o'clock in the afternoon?

Accepted Answer

Angle traced by the hour hand in 6 hours = 360 o 12 × 6 = 180 o .

Question 3

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

Accepted Answer

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.

Question 4

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

Accepted Answer

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand. To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min. 15 min. are gained in = (60/55 x 15)min =16+4/11 The hands are coincident at 16 + 4/11 min past 3

Question 5

At what time between 9 and 10 o'clock will the hands of a watch be together?

Accepted Answer

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gained in 60 min. 45 min. spaces are gained in 60 55 × 45 min or 49 1 11 min

Question 6

In 16 minutes, the minute hand gains over the hour hand by -

Accepted Answer

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minutes, the minute hand gains 330° over the hour hand. ∴ In 16 minutes, the minute hand gain over the hour hand by fraction numerator 330 degrees over denominator 60 end fraction cross times 16 degree equals 88 degree

Question 7

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

Accepted Answer

As minute hand covers, 60 degrees Minute hand covers 4800/60 = 80°

Question 8

How many times are the hands of a clock at right angle in a day?

Accepted Answer

44

Question 9

How many degrees will the minute hand move, in the same time in which the second hand move 5400 ?

Accepted Answer

Minute hand covers 5400/60 = 90°

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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 => 30 H - M 5 + M 2 degrees Here H = 4, M = 15 and the minute hand is behind the hour hand. Hence the angle = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

Question 12

At 6′o clock a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12′o clock ?

Accepted Answer

For ticking 6 times, there are 5 intervals. Each interval has time duration of 30/5 = 6 secs At 12 o'clock, there are 11 intervals, so total time for 11 intervals = 11 x 6 = 66 secs.

Question 13

At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ?

Accepted Answer

On straight line means 180 degree angle. 180 = 11/2 min – 30 hrs 180 = 11/2 m – 30 × 3 180 = 11/2 m – 90 (180 + 90) 2 = 11 m m = 540/11 = 49 1/11 minutes.

Question 14

How many times do the hands of a clock coincide in a day?

Accepted Answer

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

Question 15

In every 60 minutes, the minute hand gains -------- minutes on the hour hand

Accepted Answer

point to be remembered

Question 16

The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

Accepted Answer

Angle traced by hour hand in 13 3 hrs = 360 12 × 13 3 0 = 130 0 Angle traced by min. hand in 20 min = 360 60 × 20 0 = 120 0 Required angle = (130 - 120)º = 10º

Question 17

What time will it be 18 hours from now in India, if in the USA it is 4:15 AM? (Hint : IST = US + 9:30 hrs)

Accepted Answer

We know that the time difference between India and USA is 9 hrs 30 min. India is 9:30 hrs ahead of USA. Time in India = 4:15 + 9:30 = 13:45 PM. Required Time after 18 hrs = 13:45 + 18 hrs = 7:45 AM. Hence it is 7:45 AM on the next morning.

Question 18

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other? A. 5111 B. 15415 C. 16411 D. 4415

Accepted Answer

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand. To be coincident, it must gain 15 min. spaces. 55 min. are gained in 60 min. Then 15 min spaces are gained in = 60 55 × 15 min. Therefore, The hands are coincident at 16 4 11 min. past 3 o'clock.

Question 19

When the hands are in the opposite directions,they are ------- minute spaces apart,

Accepted Answer

30

Question 20

At 3.40, the hour hand and the minute hand of a clock form an angle of:

Accepted Answer

130

Clocks Questions