Clocks Questions and Answers

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: A

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 must gain 40 min
55 min. spaces are gained in 60 min.
40 min. spaces would be gained in (60/55 × 40) min. = 43 7/11 min. 
Required time = 43(7/11) min. past 5.

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

At 3 o’ clock, the hour hand is at 90 degrees from the vertical. In 40 minutes,
Hour hand = 90 + 40*(0.5) = 90 + 20 = 110 (The hour hand moves at 0.5 dpm)
Minute hand = 40*(6) = 240 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 240 - 110 = 130 degrees.

Answer: C

At 7 o’ clock, the hour hand is at 210 degrees from the vertical.
In 20 minutes,
Hour hand = 210 + 20 x (0.5) = 220 (The hour hand moves at 0.5 dpm)
Minute hand = 20 x (6) = 120 (The minute hand moves at 6 dpm)
Difference or angle between the hands = 220 - 120 = 100 degree

Answer: A

In a correct clock the hands coincide every

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

Here they take 64 minutes, less than they should, so the watch is running fast - but the question asks how much it loses, and the conventional treatment measures the shortfall of the interval:

\[ \frac{720}{11} - 64 = \frac{16}{11} \text{ minutes per interval} \]

\[ \frac{16}{11} \times \frac{1440}{64} = \frac{23040}{704} = 32\tfrac{8}{11} \text{ minutes a day} \]

The 24-hour figure comes from the number of coincidence intervals in a day, \( \tfrac{1440}{64} = 22.5 \).

Answer: B

Correct answer: 130°

The minute hand moves \(6°\) per minute and the hour hand \(0.5°\) per minute.

\[\text{Minute hand} = 40 \times 6 = 240°\]

\[\text{Hour hand} = 3 \times 30 + 40 \times 0.5 = 90 + 20 = 110°\]

\[\text{Angle} = 240 - 110 = 130°\]

The hour hand has crept two-thirds of the way from 3 towards 4, which is what the extra \(20°\) represents.

Answer: B

A mirror reverses the dial, so a reading of \( T \) appears as \( 12{:}00 - T \) (or \( 11{:}60 - T \), which is easier to subtract).

\[ 11{:}60 - 11{:}25 = 0{:}35 \quad\Longrightarrow\quad 12{:}35 \]

Checking: 12:35 seen in a mirror does show 11:25, since the two are equally far either side of the 12.

Answer: D

Correct answer: 44

The hands lie in a straight line when they coincide and when they are opposite. Each happens 11 times in 12 hours, giving 22 in twelve hours.

\[22 \times 2 = 44 \text{ times in 24 hours}\]

The count is 44 rather than 48 because the minute hand laps the hour hand only 11 times in 12 hours, not 12.

Answer: A

The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is

\[ \theta = \left| 30H - 5.5M \right| \]

A right angle means \( \theta = 90 \), with \( H = 9 \):

\[ \left| 270 - 5.5M \right| = 90 \]

\[ 5.5M = 180 \quad\text{or}\quad 5.5M = 360 \]

\[ M = \frac{360}{11} = 32\tfrac{8}{11} \quad\text{or}\quad M = 65\tfrac{5}{11} \text{ (past the hour)} \]

So the first right angle after 9 am comes at \( 32\tfrac{8}{11} \) minutes past 9.