# 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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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

#### View Ans & Explanation

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’