Exercise : 2


1. At what time between 3 and 4 o’clock, the hands of a clock coincide?
(a) 16411 minutes past 3
(b) 15561 minutes past 3
(c) 15560 minutes to 2
(d) 16411 minutes to 4
(e) None of these
Ans.a

Since, in one hour, two hands of a clock coincide only once, so, there will be value.

Required time T = 211(H × 30 + A°) minutes past H.

Here H = initial position of hour hand = 3(Since 3 o’clock)

A° = required angle = 0°(Since it coincides)

T = 211(3 × 30 + 0) minutes past 3

= 16411 minutes past 3

2. 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?
(a) 2 p.m. on Tuesday
(b) 2 p.m. on Wednesday
(c) 3 p.m. on Thursday
(d) 1 p.m. on Friday
(e) None of these
Ans.b

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

∴ The watch gains (2 + 445) min.

or 345 min. in 170 hrs.

Now, 345 min. are gained in 170 hrs.

∴ 2 min. are gained in (170 × 534 × 2)hrs. = 50 hrs

∴ 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.

3. If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds?
(a) 332
(b) 15
(c) 12
(d) 22
(e) None of these
Ans.b

In order to strike 12, there are 11 intervals of equal time

= 3311 = 3 seconds each

Therefore, to strike 6 it has 5 equal intervals, it requires 5 × 3 = 15 sec.

4. At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?
(a) 5 min. past 7
(b) 5211 min. past 7
(c) 5311 min. past 7
(d) 5511 min. past 7
(e) None of these
Ans.d

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 o’clock, they are 25 min. spaces apart.

∴ Minute hand will have to gain only 5 in. spaces.

55 min.spaces are gained in 60 min.

5 min. spaces are gained in (6055 × 5)min. = 5511 min.

∴ Required Time = 5511 min. past 7

5. At what time between 8 and 9 o’clock will the hands of a watch be in straight line but not together?
(a) 101110 min. past 8
(b) 101011 min. past 8
(c) 111011 min. past 8
(d) 121011 min. past 8
(e) None of these
Ans.b

At 8 o’clock, the hands of the watch are 20 min. spaces apart.

To be in straight line but not together they will be 30 min. space apart.

∴ Minute hand will have to gain 10 min. spaces 55 min.spaces are gained in 60 min.

10 min. spaces will be gained in (6055 × 50) min or 101011 min

∴ Required time = 101011 min. past 8

6. At what time between 5.30 and 6 will the hands of a clock beat right angles?
(a) 43511 min. past 5
(b) 43711 min. past 5
(c) 40 min. past 5
(d) 45 min. past 5
(e) None of these
Ans.b

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 (6055 × 40) min = 43711 min.

∴ Required time = 43711 min. past 5

7. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25.
(a) 45°
(b) 3712°
(c) 4712°
(d) 46°
(e) None of these
Ans.c

Angle traced by the hour hand in 12 hours = 360°

Angle traced by it in 3 hrs 25 min. i.e. 4112 hrs.

= (36012 × 4112)° = 10212°

Angle traced by it in 25 min. = (36060 × 25)° = 150°

Required angle = (150° × 10212°) = 4712°

8. How much does a watch lose per day, if its hands coincide every 64 minutes?
(a) 32811 min.
(b) 36511 min.
(c) 90 min.
(d) 96 min.
(e) None of these
Ans.a

55 min. spaces are covered in 60 min.

60 min. spaces are covered in (6055 × 60) min.

= 65511 min.

Loss in 64 min. = (65511 - 64) = 1611 min.

Loss in 24 hrs. = (1611 × 164 × 24 × 60) min = 32811 min.

9. An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?
(a) 144°
(b) 150°
(c) 168°
(d) 180°
(e) None of these
Ans.b

Angle traced by the hour hand in 6 hours

= (36012 × 6)° = 180°

10. The first Republic Day of India was celebrated on 26th January, 1950. It was :
(a) Tuesday
(b) Wednesday
(c) Thursday
(d) Friday
(e) None of these
Ans.c

26th Jan., 1950 = (1949 years + Period from 1st Jan.,1950 to 26th Jan., 1950)

1600 years have 0 odd day. 300 years have 1 odd day.

49 years = (12 leap years + 37 ordinary years)

= [(12 × 2) + (37 × 1)] odd days = 61 odd days

= 5 odd days.

Number of days from 1st Jan. to 26th Jan. = 26

= 5 odd days

Total number of odd days = (0 + 1 + 5 + 5) = 11

= 4 odd days

∴ The required days was ‘Thursday’