Question 1

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?

Accepted Answer

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. 145 6 hrs of this clock = 24 hours of the correct clock. 29 hours of this clock = 24 * 6 145 * 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.

Question 2

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

Accepted Answer

4 o'clock, the hands of the watch are 20 min. spaces apart. To be in opposite directions, they must be 30 min. spaces apart. Minute hand will have to gain 50 min. spaces. 55 min. spaces are gained in 60 min 50 min. spaces are gained in 60 55 × 50 min. or 54 6 11 Required time = 54 6 11 min. past 4.

Question 3

A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?

Accepted Answer

This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains 5 + 5 48 60 min in a time of (7×24)+12 = 180 hours. To show the correct time, it has to gain 5 min. 54 5 m i n → 180 h o u r s 5min -> 5 54 2 × 180 83 1 3 h r s = 72 h r s + 11 1 3 h r s = 3 d a y s + 11 h r s + 20 m i n So the correct time will be shown on wednesday at 7:20 PM

Question 4

A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day?

Accepted Answer

Time from 5 am. on a day to 10 pm. on 4th day = 89 hours. Now 23 hrs 44 min. of this clock = 24 hours of correct clock. 356/15 hrs of this clock = 24 hours of correct clock 89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock. = 90 hrs of correct clock. So, the correct time is 11 p.m.

Question 5

An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

Accepted Answer

Angle traced by the hour hand in 6 hours=(360/12)*6

Question 6

At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ?

Accepted Answer

In this type of problems the formuae is (5*x+ or - t)*12/11 Here x is replaced by the first interval of given time. Here x is 5. t is spaces apart Case 1 : (5*x + t) * 12/11 (5*5 + 3) * 12/11 28 * 12/11 = 336/11= 31 5 11 min therefore the hands will be 3 min apart at 31 5/11 min past 5. Case 2 : (5*x - t) * 12/11 (5*5 -3 ) * 12/11 22 *12/11 = 24 min therefore the hands will be 3 min apart at 24 min past 5

Question 7

Find the angle between the hour hand and the minute hand of a clock when the time is 3.25

Accepted Answer

At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins. Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5° Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5°

Question 8

The angle between the minute hand and the hour hand of a clock when the time is 8:30

Accepted Answer

Angle traced by hour hand in 17/2 hrs = 360 12 × 17 2 o = 255 Angle traced by min hand in 30 min = 360 60 × 30 o = 180 Therefore, Required angle = (255 - 180) = 75 o

Question 9

How much does a watch lose per day, if its hands coincide ever 64 minutes?

Accepted Answer

55min spaces are covered in 60min 60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min. loss in 64min=(65+5/11)- 64 =16/11 Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.

Question 10

Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together ?

Accepted Answer

In this type of problems the formulae is 5 x - 30 × 12 11 x is replaced by the first interval of given time Here i.e 8 5 * 8 - 30 * 12 11 = 120 11 min Therefore the hands will be in the same straight line but not together at 120 11 min.past 8.

Question 11

At what time between 5.30 and 6 will the hands of a clock be at right angles?

Accepted Answer

At 5 o'clock, the hands are 25 min. spaces apart. To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces. 55 min. spaces are gained in 60 min 40 min. spaces are gained in 60 55 × 40 min

Question 12

What time between 4 and 5 o'clock will the hands of a clock be at rightangle?

Accepted Answer

this type of problems the formulae is (5*x + or -15)*(12/11) Here x is replaced by the first interval of given time here i.e 4 Case 1 : (5*x + 15)*(12/11) (5*4 +15)*(12/11) (20+15)*(12/11) 35*12/11=420/11=38 2/11 min. Therefore they are right angles at 38 2/11 min .past4 Case 2 : (5*x-15)*(12/11) (5*4-15)*(12/11) (20-15)*(12/11) 5*12/11=60/11 min=5 5/11min Therefore they are right angles at 5 5/11 min.past4.

Question 13

A watch which gains uniformly is 2 minutes low at noon on monday and is 4 min.48 sec fast at 2 p.m on the following monday. when was it correct ?

Accepted Answer

Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours Therefore, The watch gains 2 + 4 4 5 min. or 34/5 min. in 170 hrs. Now, 34/5 min. are gained in 170 hrs. Therefore, 2 min are gained in 170 × 5 34 × 2 hrs = 50 hrs Therefore, Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at 2 p.m on wednesday.

Question 14

A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day ?

Accepted Answer

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour. From 8 AM to 10 PM on the same day, time passed is 14 hours. In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds. So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

Question 15

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

Accepted Answer

55 min. spaces are covered in 60 min. 60 min. spaces are covered in (60x60/55)min. Loss in 64 min. = ((65x5/11) - 64) = 16/11 min. Loss in 24 hrs = (16x1x 24 x 60)/(11x64) min. = 32 8/11 min

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