# Clocks – Logical Reasoning for Competition exams

(01) What is the angle between minute and hour hand at 11:10?

(a) 265 \degree \\\ \\ (b) 175 \degree \\\ \\ (c) 85 \degree \\\ \\  (d) 95 \degree \\ \\

When\ hour\ hand\ completes\ a\ round,\ then\ it\ crosses\ 12h\ space \\\ \\ 12h\ =\ 360\ \degree \\\ \\ 1\ h = \frac{360}{12} =30\degree \\\ \\ 1h=30 \degree \\\ \\ 60 \ min = 30 \ degree \\\ \\ 1 \ min=\frac{30}{60} =\left(\frac{1}{2}\right) \degree \\\ \\ Angle\ traced\ by\ hour\ hand\ per\ minute\ = \ \left(\frac{1}{2}\right) \degree \\\ \\ Angle \ traced\ by\ hour\ hand\ in\ 11h \ 10 min\ =[( 11\times 60) +10] \times \frac{1}{2} \degree \\ \\ =\left(\frac{670}{2}\right) =335\degree \\\ \\ \\\ \\ Angle\ traced\ by\ minute\ hand\ per\ minute =6\degree \\\ \\ Angle\ traced\ by\ minute\ hand\ in\ 10\ minutes =10\times 6=60\degree \\\ \\ \\\ \\ \\\ \\ Required\ Angle\ =\ 335-60 \ = \ 275 \degree \\\ \\

But 275 is more than 180 hence we subtract this angle from 360.

So Angle =360 – 275= 85 degree

Option (c) is the right answer

(02) What is the angle between minute and hour hand at 3:56?

(a) 152\degree \\\ \\ (b) 228\degree \\\ \\ (c) 360\degree \\\ \\ (d) 142\degree \\\ \\ Read Solution

Sol: When hour hand completes a round, then it crosses 12h space

12\ h=360\degree \\\ \\ 1\ h=\frac{360}{12} =30\degree \\\ \\ 1\ h=30\degree \\\ \\ 60\ min\ =30\degree \\\ \\ 1\ min=\frac{30}{60} =\left(\frac{1}{2}\right) \degree \\\ \\ Angle\ traced\ by\ hour\ hand\ per\ minute\ =  \left(\frac{1}{2}\right) \degree \\\ \\ Angle\ traced\ by\ hour\ hand\ in\ 3h\ 56\ min =[( 3\times 60) +56] \times \frac{1}{2} \degree \\\ \\ =\left(\frac{236}{2}\right) =118\degree \\\ \\ \\\ \\

Angle traced by minute hand per minute=6 degree
Angle traced by minute hand in 56 minutes =56 * 6= 336 degree

Required Angle =336-118 =218 degree

But 218 is more than 180 hence we subtract this angle from 360.

So Angle =360-218=142 degree

Option (d) is the right answer

(03). At what time between 6 to 7 O’ clock minute and hour hand coincide?

(a) 6:38\frac{2}{11} \\\ \\ (b) 6:43\frac{7}{11} \\\ \\ (c) 6:32\frac{8}{11} \\\ \\  (d) 6:5\frac{5}{11} \\\ \\ Read Solution

Sol: Here is a formula for finding when both hands are together=
H:\left( H\times 5\pm \frac{Angle}{6}\right) \times \frac{12}{11}

Where, H=previous hour=6

Angle= 0 degree (because it coincide)

So,

⟹ 6:\left( 6\times 5\pm \frac{0}{6}\right) \times \frac{12}{11} \\\ \\ ⟹ 6:( 30) \times \frac{12}{11} \\\ \\ ⟹ 6:\frac{360}{11}\\\ \\ ⟹ 6:32\frac{8}{11} \\\ \\

Option (c) is the right answer

(04). The minute hand of a clock overtakes the hour hand at intervals of 66 minutes of correct time. How much a day does the clock gain or lose?

(a) 11\frac{109}{121} \ minute\ gain \\\ \\ (b) 11\frac{109}{121} \ minute\ loss \\\ \\ (c) 11\frac{117}{121} \ minute\ gain \\\ \\ (d) 11\frac{117}{121} \ minute\ loss \\\ \\ Read Solution

Use the following formula for this type of questions:
\left(\frac{720}{11} -x\right)\left(\frac{60\times 24}{x}\right) min \\\ \\ Here \ x \ = \ 66 \ minutes \\\ \\ According\ to\ the\ question\\\ \\ ⟹ \left(\frac{720}{11} -66\right)\left(\frac{60\times 24}{66}\right) min \\\ \\ ⟹ \left(\frac{720-66\times 11}{11}\right)\left(\frac{10\times 24}{11}\right) \\\ \\ ⟹ \left(\frac{720-726}{11}\right)\left(\frac{240}{11}\right) \\\ \\ ⟹ \left(\frac{-6}{11}\right)\left(\frac{240}{11}\right) \\\ \\ ⟹ -\left(\frac{1440}{121}\right) \\\ \\ ⟹ -11\frac{109}{121} (loss\ as\ sign\ is\ negative) \\\ \\

Option (b) is the right answer

(05) A watch which loses uniformly is 3 minute fast at 6 A.M on thursday and is 3 minute 12 sec. slow at 5 P.M on upcoming wednesday. When was it correct?

(a) 9 P.M on Sunday

(b) 9 A.M on Monday

(c) 9 A.M on Sunday

(d) 8 A.M on Sunday

Sol: Number of hours between 6 A.M on thursday and 5 P.M on wednesday =155 hours

The watch goes from being 3 min fast to 3 min 12 sec slow.
So it actually loses =3 min + 3 min 12 sec=6 min 12 sec=372 seconds

From 6 AM Thursday to 5 PM Wednesday, there was a time when the clock showed correct time.
It was when the clock loses 3 Min to show the correct time

Clock lose in 1 hour = \frac{372}{155}

Number of hours required to loose 3 min(180 sec) = \frac{155\times 180}{372} =75 hrs

75 hours means 3 day + 3 hour

Thursday 6 A.M + (3 day + 3 hour) = Sunday 9 A.M

Option (c) is the right answer

(06). A clock with only dots marking 3,6,9 and 12 positions has been kept upside down in front of mirror. A person reads the time in the reflection of the clock as 4:50. What is the actual time?

(a) 08:10
(b) 01:40
(c) 04:50
(d) 10:20

Sol: For actual time we have to subtract 4:50 from 17:90 because both hands of clock are between 6 to 12.

17:90 – 4:50 = 13 : 40 = 1:40

(If hour hand lies between 6 to 12 and minute hand lies between 6 to 12 then we have to subtract time from 17:90 to get actual time.)

Option (b) is the right answer

Q7. A clock with only dots marking 3,6,9 and 12 positions has been kept upside down in front of mirror. A person reads the time in the reflection of the clock as 6:10. What is the actual time?

(a) 6:50
(b) 12:40
(c) 11:20
(d) 06:10

Sol:For actual time we have to subtract 6:10 from 17:30 because both hands of clock are between 12 to 6.

17:30 – 6:10 = 11:20

(If hour hand lies between 12 to 6 and minute hand lies between 12 to 6 then we have to subtract time from 17:30 to get actual time.)

Option (c) is the right answer

(08). If 50 minutes ago, it was 45 minutes past four O’ clock, how many minutes is it until six O’ clock?

(a) 45
(b) 15
(c) 25
(d) 35