Clocks Questions

Q:

A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?

 A) 48 min. past 12. B) 46 min. past 12. C) 45 min. past 12. D) 47 min. past 12.

Explanation:

Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.

24 hours 10 min. of this clock = 24 hours of the correct clock.

$\inline \fn_jvn \frac{145}{6}$ hrs of this clock = 24 hours of the correct clock.

29 hours of this clock = $\inline \fn_jvn (24\times \frac{6}{145}\times 29)$ hrs of the correct clock

= 28 hrs 48 min of the correct clock.

Therefore, the correct time is 28 hrs 48 min. after 8 a.m.

This is 48 min. past 12.

140 20310
Q:

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

 A) 54 past 4 B) (53 + 7/11) past 4 C) (54 + 8/11) past 4 D) (54 + 6/11) past 4

Explanation:

4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
$\inline \therefore$Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min

50 min. spaces are gained in $\inline (\frac{60}{55}\times 50)$ min. or $\inline 54\frac{6}{11}$

$\inline \therefore$ Required time = $\inline 54\frac{6}{11}$ min. past 4.

64 12868
Q:

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose?

 A) (10 + 10/143 )min B) (10 + 1/143 ) min C) (10 + 20/143 ) min D) (10 + 30/143) min

Explanation:

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.

To be together again, the minute hand must gain 60 minutes over the hour hand.

55 minutes are gained in 60 min.

60 min. are gained in [(60/55) * 60] min =$\inline 65\frac{5}{11}$ min.

But they are together after 65 min.

Therefore, gain in 65 minutes = $\inline (65\frac{5}{11}-65)$ =$\inline \frac{5}{11}$ min.

Gain in 24 hours = $\inline [\frac{5}{11}\times \frac{60\times 24}{65}]$ = 1440/143 min.

Therefore, the clock gains (10 + 10/143 )minutes in 24 hours.

19 9415
Q:

A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day?

 A) 11pm B) 12pm C) 1pm D) 2pm

Explanation:

Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.

Now 23 hrs 44 min. of this clock = 24 hours of correct clock.

356/15 hrs of this clock = 24 hours of correct clock

89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.

= 90 hrs of correct clock.

So, the correct time is 11 p.m.

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Q:

A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?

 A) 7pm on wednesday B) 20 min past 7pm on wednesday C) 15min past 7pm on wednesday D) 8pm on wednesday

Explanation:

This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast.  The watch gains $\inline \fn_jvn \small 5+5\tfrac{48}{60}$ min in a time of  (7×24)+12 = 180 hours.

To show the correct time, it has to gain 5 min.

$\inline \fn_jvn \frac{54}{5}min\rightarrow 180 \; hours$

$\inline \fn_jvn 5\; min\rightarrow ?$

$\inline \fn_jvn \Rightarrow \frac{5}{\frac{54}{5}}\times 180$

$\inline \fn_jvn 83\frac{1}{3}hrs =72hrs+11\frac{1}{3}hrs=3days+11hrs+20min$

So the correct time will be shown on wednesday at 7:20 PM