Clocks Questions and Answers

Answer: D

The clock gains 20 seconds in every 3 hours, so first count the hours.

From Thursday 2:00 am to Friday 6:30 pm is

\[ 22 + 18.5 = 40.5 \text{ hours} \]

\[ \text{gain} = 20 \times \frac{40.5}{3} = 20 \times 13.5 = 270 \text{ s} = 4 \text{ min } 30 \text{ s} \]

The clock therefore reads ahead of the true 6:30 pm:

\[ 6{:}30{:}00 + 4{:}30 = 6{:}34{:}30 \text{ pm} \]

Answer: C

In a correct clock the hands coincide every

\[ \frac{720}{11} = 65\tfrac{5}{11} \text{ minutes} \]

Here they coincide every 62 minutes, sooner than they should, so the clock is gaining.

\[ \text{gain per interval} = \frac{720}{11} - 62 = \frac{38}{11} \text{ min} \]

In 1440 minutes there are \( \tfrac{1440}{62} \) such intervals:

\[ \text{gain per day} = \frac{38}{11} \times \frac{1440}{62} = \frac{54720}{682} = 80\tfrac{80}{341} \text{ minutes} \]

Coinciding more often than every \( 65\tfrac{5}{11} \) minutes always means a fast clock; a slower interval, such as 64 minutes, would mean a loss.

Answer: B

Time from 5 am On a day to 3 pm on 8th day = 178 hours
Now 23 hrs 44 min. of this clock = 24 hours of correct clock
365/15 hrs of this clock = 24 hours of correct clock
178 hrs of this clock = (24 × 15/356 × 89) hrs of correct clock
= 180 hrs of correct clock.
So, the correct time is 5 pm.

Answer: C

In 12 hours, the hands coincide or are in opposite direction 22 times.

 In 24 hours, the hands coincide or are in opposite direction 44 times a day.

Answer: B

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 overlap about every 65 minutes, not every 60 minutes.
Therefore, The hands coincide 22 times in a day.

Answer: A

The hour hand covers \( 360^{\circ} \) in twelve hours:

\[ \frac{360}{12} = 30^{\circ} \text{ per hour} \]

\[ \frac{30}{60} = 0.5^{\circ} \text{ per minute} \]

The minute hand, by contrast, does \( 6^{\circ} \) a minute - twelve times as fast.

Answer: C

8 Seconds in 4 Minutes mean 120 Seconds (or 2 Minutes) in one hour.
From 4AM to 11PM (on the same day) = 19 hours
So, total seconds gain in 19 hours = 19 X 120 (Seconds gain per hour) = 2280 Seconds.
Now, 2280 Seconds = 38 Minutes (i.e. 2280/19 = 38)
Thus incorrect clock will show 11:38PM at 11PM.

Answer: C

The hour hand turns \( 30^{\circ} \) an hour, or \( 0.5^{\circ} \) a minute.

From noon to 5:10 is \( 5\tfrac{1}{6} \) hours:

\[ 5\tfrac{1}{6} \times 30 = 155^{\circ} \]

The extra ten minutes contribute \( 10 \times 0.5 = 5^{\circ} \), which is what lifts the answer above the whole-hour figure.

Answer: D

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.

Answer: C

Time from 8 am on Sunday to 8 pm on following Sunday = 7 days 12 hours
= 180 hours

∴ The watch gains (5 + 29/5) min or 54/5 min in 180 hours.

Now 54/5 minutes are gained in 180 hours.

∴ 5 minutes are gained in [180*(5/54)*5] hour = 83 hr 20 min
= 3 days 11 hours 20 minutes
Watch is correct 3 days 11 hours 20 minutes
after 8 AM of Sunday i.e. 7:20PM on Wednesday.