68
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:

In 16 minutes, the minute hand gains over the hour hand by -

 A) 16 deg B) 80 deg C) 88 deg D) 94 deg

Explanation:

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by

3 31
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.

4 191
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.

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

5 278
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.

5 340
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.