57
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

Answer:   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.

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.

10 72
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 =$\inline \fn_jvn \small \left ( \frac{360^{\circ}}{12} \times 6 \right )$ = $\inline \fn_jvn \small 180^{\circ}$.

Filed Under: Clocks - Quantitative Aptitude - Arithmetic Ability
Exam Prep: CAT
Job Role: Bank Clerk

8 99
Q:

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

 A) 2 p.m on Tuesday B) 2 p.m on Wednesday C) 3 p.m on Thursday D) 1 p.m on Friday

Explanation:

Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours

$\therefore$ The watch gains $\inline&space;\left&space;(&space;2+4\frac{4}{5}&space;\right&space;)$ min. or  $\inline&space;\frac{34}{5}$ min. in 170 hrs.

Now, $\inline&space;\frac{34}{5}$ min. are gained in 170 hrs.

$\inline&space;\therefore$ 2 min are gained in $\inline&space;\left&space;(&space;170\times&space;\frac{5}{34}\times&space;2&space;\right&space;)$ hrs = 50 hrs

$\inline&space;\therefore$ Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at  2 p.m on wednesday.

26 1300
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) = $\inline&space;75^{o}$

25 3051
Q:

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

 A) 11 4/11 B) 13 4/11 C) 15 4/11 D) 16 4/11