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clock

1. At what time between 3 O’clock and 4 O’clock will the two hands of a clock be together?

a) 16 4/11 min. past 3 O’clock

b) 15 4/11 min. past 3 O’clock

c) 13 4/11 min. past 3 O’clock

d) 11 4/11 min. past 3 O’clock

Sol: When the two hands of a clock are together (or coincide) the angle between them is 0°.

θ = 11/2 m − 30 h

Here, h = 3 and θ = 0°

θ = 11/2 m − 30 × 3 ⇒ 11/2 m = 90

⇒ m = 180/11 min. = 16 4/11 min.

Therefore, the hands of a clock are together at 16 4/11 min. past 3 O’clock.

Ans: a

 

2. At what time between 4 O’ clock and 5 O’ clock the minute hand and the hour hand of a clock will be perpendicular to each other?

a) 4 hrs. 38 2/11 min.          b) 4 hrs. 5 5/11 min.

c) 4 hrs. 7 2/11 min.            d) Both a and b

Sol: θ = 11/2 m − 30 h

Here, θ = 90° and h = 4

90 = 11/2 × m − 30 × 4

∴ 11/2 m = 210 ⇒ m = 420/11 min.

= 38 2/11 min.

Also, θ = 30h − 11/2 m

90 = 30 × 4 − 11/2 m

∴ 11/2 m = 30 ⇒ m = 60/11 min.

= 5 5/11 min.

Therefore, the angle between the two hands of the clock is 90°, when the time is 4 hrs. 38 2/11 min. and 4 hrs. = 5 5/11 min.

Ans: d

 

3. At 7:20, the hour hand and the minute hand of a clock form an angle of.....

a) 60°         b) 100°        c) 30°        d) 50°

Sol: The angle between the two hand of a clock at 7:20 is

θ = 30 h − 11/2 m (As 30h > 11/2 m)

here, h = 7 and m = 20

θ = 30 × 7 − 11/2 × 20 ⇒ θ = 100°

Ans: b

 

4. What angle do the hands of a clock form at 20 minutes past 2?

a) 40°    b) 30°     c) 50°      d) 60°

Sol: θ = 11/2 m − 30 h

Here, m = 20 and h = 2

θ = 11/2 × 20 − 30 × 2 ⇒ θ = 50°

Ans: c

 

5. A watch is 2 minutes slow at 2 p.m on Tuesday and is 2 minutes fast at 10 a.m on the next day. When did it show the correct time?

a) 12 a.m. Tuesday

b) 11 p.m. Tuesday

c) 12 a.m. Wednesday

d) 11 a.m. Wednesday

Sol: Time from 2 p.m on Tuesday to 10 a.m on the next day = 20 hours.

∴ The watch gains (2 + 2) min. or 4 min. in 20 hours.

∴ 2 min. are gained in (20 × 2/4) hrs = 10 hrs.

∴ Watch is correct 10 hrs. after 2 p.m on Tuesday, i.e.,

it will be correct at 12 a.m on Wednesday.

Ans: c

 

6. A clock is set to show correct time at 4 a.m. The clock gains 12 minutes in a day. What will be the correct time, when the watch indicates 4:30 p.m. day after tomorrow?

a) 5 : 00 p.m.         b) 4 : 00 p.m.         c) 6 : 00 p.m.         d) 5 : 30 p.m.

Sol: Total number of hours from 4 a.m. today to 4:30 p.m. day after tomorrow = 60.5 hours.

24 hrs. 12 min. of this clock = 24 hrs. of the correct clock (24 × 12/60) hrs. = 121/5 hrs. of this clock = 24 hrs. of the correct clock.

∴ 60.5 hrs. of this clock = 60.5 × (5×24 / 121) = 60 hrs of the correct clock

∴ The correct time i.e. 60 hours. after 4 a.m is 4:00 p.m. day after tomorrow.

Ans: b

 

7. If the time in a clock is 7 hrs. 30 min, then what time will it show in the mirror?

a) 6 hrs. 20 min.       b) 4 hrs. 30 min.

c) 3 hrs. 20 min.       d) 5 hrs. 20 min.

Sol: The time shown by the clock when it is seen in the mirror

= 12 hrs. − (7 hrs. 30 min.) = 4 hrs. 30 min.

Ans: b

 

8. The angle formed by the hour-hand and the minute-hand of a clock at 3:30 p.m. will be

a) 75°      b) 90°     c) 45°     d) 60°

Sol: 11/2 m − 30h = θ

⇒ θ = 11/2 × 30 − 30 × 3 = 75°

Ans: a

 

9. A clock losses five minutes every hour. What will be the angle traversed by the second hand in one minute?

a) 330°      b) 300°      c) 390°     d) 345°

Sol: Angle traversed by second hand in one hour = 55 × 360°

∴ Angle traversed by second hand in one minute (55 × 360°) / 60 = 330°

Ans: a

 

10. Three bells ring simultaneously at 12 noon. They ring at regular intervals of 10 minutes, 15 minutes and 25 minutes respectively. The next time when all the three bells ring together is....

a) 3:15 p.m.              b) 5:00 p.m.

c) 2:30 p.m.             d) 4:45 p.m.

Sol: LCM (10, 15, 25) = 150

∴ The time when all the three bells ring together next time is 2:30 p.m.

Ans: c

 

11. If my watch would have been 15 minutes fast, I would have reached my destination at sharp 5 a.m. At what actual time did I reach the destination?

a) 5:15 a.m.           b) 4:45 a.m.

c) 4:40 a.m.           d) 5:20 a.m.

Sol: I have reached the destination at 4:45 a.m.

Ans: b

 

12. At what time after 3:20 p.m. will the hour and minute hands of a clock make an angle of 75°?

a) 3:25 p.m.        b) 3:27 p.m.

c) 3:29 p.m.        d) 3:30 p.m.

Sol: We know the θ = |30h − 5.5m|

Thus, 75° = |30 × 3 − 5.5m|

Or, m = 30/11 and 30

Hence, the required time after 3:20 p.m. will be 3:30 p.m.

Ans: d

 

13. How many times would the hour and the minute hand of a faulty clock meet in 12 hrs if the two hands of this clock move in opposite directions?

a) 11     b) 12      c) 13       d) 14

Sol: The ratio of the speed of the hour and the minute hand is 1 : 12 and they move in the opposite direction.

Hence, they will meet 1 + 12 = 13 times.

Ans: c

Posted Date : 24-02-2021

 

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