Aptitude Clock Practice QA

Explanation:

When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.

At 7 oclock, they are 25 min. spaces apart.

$\therefore$ Minute hand will have to gain only 5 min. spaces.

55 min. spaces are gained in 60 min.

5 min. spaces are gained in$ \left(\dfrac{60}{55} \times 5\right) $min= 5$ \dfrac{5}{11} $min.

$\therefore$ Required time = 5$ \dfrac{5}{11} $min. past 7.

Explanation:

At 5 oclock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in$ \left(\dfrac{60}{55} \times 40\right) $min=43$ \dfrac{7}{11} $min.

$\therefore$ Required time = 43$ \dfrac{7}{11} $min. past 5.

Explanation:

Angle traced by hour hand in 12 hrs. = 360$^\circ$

Angle traced by it in$ \dfrac{11}{3} $hrs =$\left(\dfrac{360}{12} \times\dfrac{11}{3}\right)^\circ$ =110$^\circ$.

Angle traced by minute hand in 60 min. = 360$^\circ$

Angle traced by it in 40 min. =$ \left(\dfrac{360}{60} \times 40\right)^\circ$= 240$^\circ$.

$\therefore$ Required angle (240 - 110)$^\circ$ = 130$^\circ$

Explanation:

Angle traced by hour hand in$ \dfrac{17}{2} $hrs =$\left(\dfrac{360}{12} \times \dfrac{17}{2}\right)^\circ$= 255.

Angle traced by min. hand in 30 min. =$ \left(\dfrac{360}{60} \times 30\right)^\circ$ = 180.

$\therefore$ Required angle = (255 - 180)$^\circ$ = 75$^\circ$

Explanation:

At 4 oclock, the hands of the watch are 20 min. spaces apart.

To be in opposite directions, they must be 30 min. spaces apart.

$\therefore$ Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in$ \left(\dfrac{60}{55} \times 50\right)$min. or 54$ \dfrac{6}{11} $min.

Explanation:

To be together between 9 and 10 oclock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in$ \left(\dfrac{60}{55} \times 45\right) $min or 49$ \dfrac{1}{11} $min.

$\therefore$ The hands are together at 49$ \dfrac{1}{11} $min. past 9.

Explanation:

At 3 oclock, 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.

15 min. are gained in$ \left(\dfrac{60}{55} \times 15\right) $min=16$ \dfrac{4}{11} $min.

$\therefore$ The hands are coincident at 16$ \dfrac{4}{11} $min. past 3.

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$ \left(2 + 4\dfrac{4}{5} \right) $min.or$ \dfrac{34}{5} $min. in 170 hrs.

Now,$ \dfrac{34}{5} $min. are gained in 170 hrs.

$\therefore$ 2 min. are gained in$ \left(170 \times\dfrac{5}{34} \times 2\right) $hrs= 50 hrs.

$\therefore$ 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.

Explanation:

There are 3 intervals when the clock strikes 4

Time taken for 3 intervals = 9 seconds

Time taken for 1 interval =$\dfrac{9}{3}$=3 seconds

In order to strike 12, there are 11 intervals.

Hence time needed =3 $\times$ 11 = 33 seconds

Explanation:
The LCM of 50 and 48 being 1200, the two clocks will ring again after 1200 seconds.