Arithmetic aptitude :: Clocks :: Clocks_type1

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How many times do the hands of a clock coincide in a day?

Answer:

Explanation:

c) The hands of a clock coincide 11 times in every 12 hours. Since between 11 and 1 they coincide only once, (i.e) at 12 o'clock.

.'. The hands coincide 22 times in a day.

At what time will the hands of a clock be coincident between 3 and 4 o'clock?

Answer:

Explanation:

At 3 o'clock the 2 hands are 15 min. spaces apart.
The minute hand will have to gain 15 min. to be coincident. 55 min. spaces are gained in = 60 min.

There for, 15 min. spaces are gained in (60/55) X 15 = (180/11) = 16(4/11) min.

16 (4/11) min past 3

A clock gains uniformly and is slow by 8 minutes at 10 a.m. on Sunday and is 6 minutes 24 seconds fast at 10 p.m. on the following Sunday. When did the clock show correct time?

Answer:

Explanation:

Time from 10 a.m on sunday to 10 p.m on following sunday= 7 days 12 hours=180 hours.

The clock gains ( 8+ 6 (24/60)) min

= 8+ 6(2/5)= 8+(32/5)=(72/5) min in 180 hours.

there for, 8 min are gained in =180 X (5/72) X 8 hrs=100hrs.

there for, The Clock is correct, 4 days 4 hours after 10 a.m on sunday.

(i.e) Thursday 2 p.m

At what time between 7 and 8 o'clock will the angle between the two hands of a clock be 0°?

Answer:

Explanation:

At 7 o'clock the hour hand is at 7 and the minute hand is at 12,
(i.e) they are 35 min. spaces apart. To be together, the minute hand must gain 35 min. over the hour hand.
55 min are gained in 60 min.

25 min will be gained in = (60/55) X 35

                                   =(12/11) X 35= 420/11= 38(2/11) min

i.e 38(2/11) min past 7 (i.e) =7.38

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