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Home > Practice > Arithmetic Aptitude > Clocks > Miscellaneous

1. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?

A. 144º

B. 150º

C. 168º

D. 180º

Discuss

Solution:

\begin{aligned} Angle traced be the hour hand in 6 hours \\ = {(\frac{360}{12} \times 6)}^{\circ} = 180^{\circ} \end{aligned}

2. The reflex angle between the hands of a clock at 10.25 is:

A. 180º

B. $192 {\frac{1}{2}}^{\circ}$

C. 195º

D. $197 {\frac{1}{2}}^{\circ}$

Discuss

Solution:

Angle traced by hour hand in

\frac{125}{12}

hrs

\begin{aligned} = {(\frac{360}{12} \times \frac{125}{12})}^{\circ} \\ = 312 {\frac{1}{2}}^{\circ} \end{aligned}

Angle traced by minute hand in 25 min

\begin{aligned} = {(\frac{360}{60} \times 25)}^{\circ} \\ = 150^{\circ} \end{aligned}

\begin{aligned} ∴ Reflex angle \\ = 360^{\circ} - {(312 \frac{1}{2} - 150)}^{\circ} \\ = 360^{\circ} - 162 {\frac{1}{2}}^{\circ} \\ = 197 {\frac{1}{2}}^{\circ} \end{aligned}

3. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

A. 145º

B. 150º

C. 155º

D. 160º

Discuss

Solution:

Angle traced by hour hand in 12 hrs =

360^{\circ}

Angle traced by hour hand in 5 hrs 10 min. i.e.,

\begin{aligned} \frac{31}{6} hrs = {(\frac{360}{12} \times \frac{31}{6})}^{\circ} \\ = 155^{\circ} \end{aligned}

4. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

A. $59 \frac{7}{12}$ min. past 3

B. 4 p.m.

C. $58 \frac{7}{11}$ min. past 3

D. $2 \frac{3}{11}$ min. past 4

Discuss

Solution:

Time from 7 a.m. to 4:15 p.m. = 9 hrs 15 min. =

\frac{37}{4}

hrs
3 min. 5 sec. of this c;ocl = 3 min. of the correct clock
⇒

\frac{37}{720}

hrs. of this clock =

\frac{1}{20}

hrs of the correct clock
⇒

\frac{37}{4}

hrs. of this clock =

(\frac{1}{20} \times \frac{720}{37} \times \frac{37}{4})

hrs. of the correct clock
= 9 hrs. of the correct clock
∴ The correct time is 9 hrs. after 7 a.m. i.e., 4 p.m.

5. How much does a watch lose per day, if its hands coincide every 64 minutes?

A. $32 \frac{8}{11}$ min.

B. $36 \frac{5}{11}$ min.

C. 90 min.

D. 96 min.

Discuss

Solution:

\begin{aligned} 55 min . spaces are covered in 60 min \\ 60 min . spaces are covered in \\ = (\frac{60}{55} \times 60) min . \\ = 65 \frac{5}{11} min . \\ Loss in 64 min . \\ = 65 \frac{5}{11} - 64 = \frac{16}{11} min . \\ Loss in 24 h r s . \\ = (\frac{16}{11} \times \frac{1}{64} \times 24 \times 60) min . \\ = 32 \frac{8}{11} min . \end{aligned}

6. 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. $5 \frac{2}{11}$ min. past 7

C. $5 \frac{3}{11}$ min. past 7

D. $5 \frac{5}{11}$ min. past 7

Discuss

Solution:

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 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in

\begin{aligned} = (\frac{60}{55} \times 5) min . \\ = 5 \frac{5}{11} min . \\ ∴ Required time = 5 \frac{5}{11} min . past 7 \end{aligned}

7. At what time between 5:30 and 6 will the hands of a clock be at right angles?

A. $43 \frac{5}{11}$ min. past 5

B. $43 \frac{7}{11}$ min. past 5

C. 40 min. past 5

D. 45 min. past 5

Discuss

Solution:

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

\begin{aligned} = (\frac{60}{55} \times 40) min . \\ = 43 \frac{7}{11} min . \\ ∴ Required time = 43 \frac{7}{11} min . past 5 \end{aligned}

8. The angle between the minute hand and the hour hand of a clock when the time is 4:20, is:

A. 0º

B. 10º

C. 5º

D. 20º

Discuss

Solution:

\begin{aligned} Angle traced by hour hand in \frac{13}{3} hrs \\ = {(\frac{360}{12} \times \frac{13}{3})}^{\circ} = 130^{\circ} \\ Angle traced by min . hand in 20 min \\ = {(\frac{360}{60} \times 20)}^{\circ} = 120^{\circ} \\ ∴ Required angle \\ = {(130 - 120)}^{\circ} \\ = 10^{\circ} \end{aligned}

9. At what angle the hands of a clock are inclined at 15 minutes past 5?

A. $58 {\frac{1}{2}}^{\circ}$

B. $64^{\circ}$

C. $67 {\frac{1}{2}}^{\circ}$

D. $72 {\frac{1}{2}}^{\circ}$

Discuss

Solution:

\begin{aligned} Angle traced by hour hand in \frac{21}{4} hrs \\ = {(\frac{360}{12} \times \frac{21}{4})}^{\circ} = 157 {\frac{1}{2}}^{\circ} \\ Angle traced by min . hand in 15 min \\ = {(\frac{360}{60} \times 15)}^{\circ} = 90^{\circ} \\ ∴ Required angle \\ = {(157 \frac{1}{2})}^{\circ} - 90^{\circ} \\ = 67 {\frac{1}{2}}^{\circ} \end{aligned}

10. At 3:40, the hour hand and the minute hand of a clock form an angle of:

A. 120°

B. 125°

C. 130°

D. 135°

Discuss

Solution:

\begin{aligned} Angle traced by hour hand in 12 hrs = 36 0^{\circ} \\ Angle traced by it in \frac{11}{3} hrs \\ = {(\frac{360}{12} \times \frac{11}{3})}^{\circ} = 110^{\circ} \\ Angle traced by min . hand in 60 min = 36 0^{\circ} \\ Angle traced by it in 40 min . \\ = {(\frac{360}{60} \times 40)}^{\circ} = 240^{\circ} \\ ∴ Required angle \\ = {(240 - 110)}^{\circ} = 130^{\circ} \end{aligned}

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