Sol : Option A
Formula used= θ=(11/2)M -30H where, H= hours, M= minutes
H= 5 , M= 40
Required angle, θ=(11/2)40 -30×5 = 70°

Q.2. At what time between 2 and 3 o’clock will the hands of a clock be together?

A. 10(10/11)min. past 2

B. 10 min. past 2

C. 20(10/11)min. past 2

D. 12 min. past 2

Sol : Option A
At 2 o’ clock, the hour hand is at 2 and the minute hand is at 12. So, they are 10 min. spaces apart. To be together, the minute hand must gain 10 minutes over the hour hand.
Now, 55 minutes are gained by it in 60 min. So, 10 minutes will be gained in (60/55)×10 min.
= 10(10/11) min
The hands will coincide at 10(10/11) min. past 2.

Q.3. What when the time is 6:32, then what is the angle b/w the hour hand & the minute hand of a clock?

A. 2°

B. 4°

C. 8°

D. 12°

Sol : Option B
Formula used = θ = 30H - (11/2)M where, H= hours, M= minutes
H= 6 , M= 32
Required angle, θ = 30×6 - (11/2)32 = 4°

Q.4. How many times do the hands of a clock coincide in a day?

A. 20

B. 21

C. 22

D. 24

Sol : Option C/strong>
The hands of a clock coincide 11 times in every 12 hours (since between 11 and 1, they coincide only once, i.e. at 12 o’ clock). The hands coincide 22 times in a day.

Q.5. At what time between 1 and 2 o’ clock will the hands of a watch makes an angle of 180°

A. 35(5/11) min. past 1

B. 40 min. past 1

C. 50(4/11) min. past

D. 38(2/11) min. past 1

Sol : Option D
Assume that minute hand will be at 7 then hands make an angle of 180°. it contains 7 equal parts. Each part= 30°
Total angle= 7 ×30°= 210°
11/2° gain in 1 minutes
210° gain in =(2/11)×210=420/11=38(2/11) min. past 1

Q.6. At what time between 6 and 7 are the hands of a clock 8 minutes apart?

A. 24 min past 6

B. 21 min past 6

C. 18min past 6

D. 20 min past 6

Sol : Option A
Between x and (x + 1) O’clock, the 2 hands will be t min apart at (5x ± t)(12/11) min past x. Between 6 and 7 O’clock, the 2 hands will be 8 min. apart at (5 6 –8) (12/11) = 264/11 =24 min past 6.

Q.7. A clock is set right at 1 pm. If it gains one minute an hour, what is the true time when the clock indicates 6 pm the same day?

A. 5(7/61) min past 5

B. 55(8/61) min past 5

C. 55(8/61) min past 5

D. 56(5/61) min past 5

Sol : Option B
Clock gains one minute an hour. In 61 min, it shows 1 min less. In 5 hrs (300 min) it will show 300/61 min less actual time will be 6 –(300/61) i.e. 55(5/61) min past 5 pm.

Q8. The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much does the clock gain or lose in 12 hours?

A. 16(5/11) min

B. 16(4/11) min

C. 16(6/11) min

D. 16(7/11) min

Sol : Option B
60 min are gained in (60/55)×60 = 65(5/11) min. But they are together after 64 min.
Gain in 65 min.= 65(5/11) -64 = (16/11)m Gain in 12 hrs = (16/11) × (12×60/64) = 180/11 =16(4/11) min.

Q9. Find the time between 3 and 4 will the hands of a watch point in the opposite direction?

A. 49(1/11) min past 3

B. 49(3/11) min past 3

C. 49(2/11) min past 3

D. 49(4/11) min past 3

Sol : Option A
Between x and (x + 1) O’clock, the 2 hands are in opposite directions at (5x + 30)(12/11) min past x.
So, between 3 and 4, 2 hands will be in opposite directions at (5 3 + 30)(12/11)
= (45)(12/11) = 540/11 = 49(1/11) min past 3.

Q10. At what time between 5 and 6 pm will the hands of a clock be coincident?

A. 21(8/11) min past 4

B. 32(8/11) min past 5

C. 21(5/11) min past 4

D. 21(4/11) min past 4

Sol : Option B
Between 5 and 6 pm, hands of a clock will be together at 5 6 (12/11) min past 5 i.e. 360/11 = 32(8/11) min past 5.