# Exercise : 2

^{4}⁄

_{11}minutes past 3

(b) 15

^{5}⁄

_{61}minutes past 3

(c) 15

^{5}⁄

_{60}minutes to 2

(d) 16

^{4}⁄

_{11}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 = ^{2}⁄_{11}(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 = ^{2}⁄_{11}(3 × 30 + 0) minutes past 3

= 16^{4}⁄_{11} minutes past 3

(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 + 4^{4}⁄_{5}) min.

or ^{34}⁄_{5} min. in 170 hrs.

Now, ^{34}⁄_{5} min. are gained in 170 hrs.

∴ 2 min. are gained in (170 × ^{5}⁄_{34} × 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.

^{33}⁄

_{2}

(b) 15

(c) 12

(d) 22

(e) None of these

**Ans.b**

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

= ^{33}⁄_{11} = 3 seconds each

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

(b) 5

^{2}⁄

_{11}min. past 7

(c) 5

^{3}⁄

_{11}min. past 7

(d) 5

^{5}⁄

_{11}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 (^{60}⁄_{55} × 5)min. = 5^{5}⁄_{11} min.

∴ Required Time = 5^{5}⁄_{11} min. past 7

^{11}⁄

_{10}min. past 8

(b) 10

^{10}⁄

_{11}min. past 8

(c) 11

^{10}⁄

_{11}min. past 8

(d) 12

^{10}⁄

_{11}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 (^{60}⁄_{55} × 50) min or 10^{10}⁄_{11} min

∴ Required time = 10^{10}⁄_{11} min. past 8

^{5}⁄

_{11}min. past 5

(b) 43

^{7}⁄

_{11}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 (^{60}⁄_{55} × 40) min = 43^{7}⁄_{11} min.

∴ Required time = 43^{7}⁄_{11} min. past 5

(b) 37

^{1}⁄

_{2}°

(c) 47

^{1}⁄

_{2}°

(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. ^{41}⁄_{12} hrs.

= (^{360}⁄_{12} × ^{41}⁄_{12})° = 102^{1}⁄_{2}°

Angle traced by it in 25 min. = (^{360}⁄_{60} × 25)° = 150°

Required angle = (150° × 102^{1}⁄_{2}°) = 47^{1}⁄_{2}°

^{8}⁄

_{11}min.

(b) 36

^{5}⁄

_{11}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 (^{60}⁄_{55} × 60) min.

= 65^{5}⁄_{11} min.

Loss in 64 min. = (65^{5}⁄_{11} - 64) = ^{16}⁄_{11} min.

Loss in 24 hrs. = (^{16}⁄_{11} × ^{1}⁄_{64} × 24 × 60) min = 32^{8}⁄_{11} min.

(b) 150°

(c) 168°

(d) 180°

(e) None of these

**Ans.b**

Angle traced by the hour hand in 6 hours

= (^{360}⁄_{12} × 6)° = 180°

(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’