Arithmetic aptitude :: Clocks :: Clocks_type1

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What is the angle covered by the minute-hand in 27 minutes?

Answer:

Explanation:

["he minute hand covers 6° in one minute. Hence it :overs 27 x 6 = 162° in 27 minutes.        

At what time between 4 and 5 are the hands of a clock 4 minutes apart?

Answer:

Explanation:

Case I:
Minute hand is 4 minute spaGes behind the hour hand.
In this case, the minute hand has to gain = 20-4 = 16 min. spaces
55 min. are gained in 60 min.
16 min. are gained in (60/55) x 16 min = (192/11) = 17(5/11) min.

=17(5/11) min past 4.

Case II.

Minute hand is 4 minute spaces ahead of the hour hand.
In this case, the minute hand has to gain 20+4=24 min. spaces
55 min. are gained in 60 min.

There for, 24 min are gained in (60/55) x 24 = (288/11) = 26(2/11) min.

=26(2/11) min. past 4.

The hands of a clock coincide after every 66 min. of correct time. How much is the clock fast or slow in 24 hours?

Answer:

Explanation:

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 min.
To be together again the clock must gain 60 min. over the hour hand.
55 min. are gained in 60 min.

6-0 min. are gained in (60/55) x 60 = 65(5/11) min.

But they are together after 66 min.

Lose in 66 min. = 66-(65(5/11))=(6/11).

Lose in 24 hours =[ (6/11) x ((60 x 24)/66)] min = 1440/121 = 11(109/121).

There for, the clock is slow by 11(109/121) min

Anoop's watch, which gains uniformly, is 2 minutes slow at noon on Sunday, and is 4 minutes and 48 seconds fast at 2 p.m. on the following Sunday. When was it correct?

Answer:

Explanation:

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

There for the Watch Gains 2+(4(48/60))=2+(4(4/5))=(34/5) min in 170 hours.

(34/5) min is gained in 170 hours.

There for, 2 min is gained in 170 x (5/34) x 2=50 hrs.

.'. The watch is correct after 2 days 2 hrs (i.e) at 2 p.m on Tuesday.

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much the clock gain or lose in a day?

Answer:

Explanation:

In a correct clock, the minute hand gains 55 min. spaces over
the hour hand in 60 min.
55 min. are gained in 60 min.

60 min. are gained in (60/55) X 60=65(5/11) min

But, they are together after 65 min.

There fore, Gain in 65 min=(65(5/11)-65) =5/11.

Gain in 24 hours = (5/11) X ((60 X 24)/65)=10(10/43) min.

There fore, The clock gains 10(10/43) min. in a day.

• Clocks - Clocks_type1