27
Q:

# The angle between the minute hand and the hour hand of a clock when the time is 8:30

 A) 80 Degrees B) 75 Degrees C) 60 Degrees D) 105 Degrees

Explanation:

Angle traced by hour hand in $\inline&space;\frac{17}{2}$ hrs = $\inline&space;\left&space;(&space;\frac{360}{12}\times&space;\frac{17}{2}&space;\right&space;)^{o}$ = 255

Angle traced by min hand in 30 min = $\inline&space;\left&space;(&space;\frac{360}{60}\times&space;30&space;\right&space;)^{o}$ = 180

$\inline&space;\therefore$ Required angle = (255 - 180) = $\inline&space;75^{o}$

Q:

At 6′o clock a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12′o clock ?

 A) 66 sec B) 55 sec C) 36 sec D) 24 sec

Explanation:

For ticking 6 times, there are 5 intervals.

Each interval has time duration of 30/5 = 6 secs

At 12 o'clock, there are 11 intervals,
so total time for 11 intervals = 11 x 6 = 66 secs.

4 93
Q:

At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ?

 A) 3:15 2/8 B) 3:49 C) 3:49 1/11 D) 3:51

Explanation:

On straight line means 180 degree angle.
180 = 11/2 min – 30 hrs
180 = 11/2 m – 30 × 3
180 = 11/2 m – 90
(180 + 90) 2 = 11 m
m = 540/11 = 49 1/11 minutes.

$\inline \fn_jvn \therefore time = 3: 49 \frac{1}{11}$

5 181
Q:

A watch which gains uniformly is 2 minutes low at noon on Tuesday and is 4 min 48 sec fast at 2 p.m. on the following Tuesday. When was it correct ?

 A) 12 p.m. on Wednesday B) 2 p.m. on Thursday C) 3 p.m. on Thursday D) 2 p.m. on Wednesday

Explanation:

Time from 12 p.m. on Tuesday to 2 p.m. on the following Tuesday = 7 days 2 hours.
= 170 hours.
The watch gains = (2 + 4 x 4/5) min
= 34/5 min. in 170 hrs.
Now, 34/5 min are gained in 170 hrs.
Then, 2 min are gained in (170 x 5/34 x 2) hrs.
Watch is correct after 2 days 2 hrs after 12 p.m. on Tuesday, i.e., it will be correct at 2 p.m. on Thursday.

5 209
Q:

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

$\inline \fn_jvn \small A. \: 5\frac{1}{11}$

$\inline \fn_jvn \small B.\: 15\frac{4}{15}$

$\inline \fn_jvn \small C. \: 16\frac{4}{11}$

$\inline \fn_jvn \small D.\: 4\frac{4}{15}$

 A) Option A B) Option B C) Option C D) Option D

Explanation:

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

Then 15 min spaces are gained in $\inline \fn_jvn \small \left ( \frac{60}{55}\times 15 \right ) min$ = $\inline \fn_jvn \small 16\tfrac{4}{11}$ min.

$\fn_jvn&space;\small&space;\therefore$ The hands are coincident at  $\inline \fn_jvn \small 16\tfrac{4}{11}$ min. past 3 o'clock.

12 263
Q:

An accurate clock shows 7 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 3 o'clock in the afternoon?

 A) 144º B) 168º C) 180º D) 150º

Explanation:

Angle traced by the hour hand in 6 hours =$\inline \fn_jvn \small \left ( \frac{360^{\circ}}{12} \times 6 \right )$ = $\inline \fn_jvn \small 180^{\circ}$.