Notes - Time and Clocks
Category : 12th Class
Time and Clocks
Time and Clock
The face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.
A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
On the other hand, if it indicates \[7:45\], when the correct time is 8, it is said to be 15 minutes too slow.
Example:
(a) 20 minutes (b) 29 minutes
(c) 30 minutes (d) 35 minutes
(e) None of these
Ans. (b)
Explanation: Hours between \[3:30\] pm and 6 am are \[=14\frac{1}{2}\].
So, numbers of minutes gained will be \[=14\frac{1}{2}\,\,\times \,\,2\,\,=\,\,29\] minutes.
(a) Dec 30, 1978 noon (b) Dec 25, 1978 noon
(c) Dec 27, 1978 noon (d) Dec 26, 1978 noon
(e) None of these
Ans. (c)
Explanation: The first watch gains on the second watch \[1+1=2\] minutes in a day.
The watch will indicate the same time when the one has gained 12 hours on the other
As 2 minutes is gained in one day.
So 12 hours is gained \[=1/2\times 12\times 60=360\text{ }days\]
Counting 360 days from 1st Jan 1978, we get Dec 27, 1978.
(a) 0 (b) 1
(c) 2 (d) 3
(e) None of these
Ans. (b)
Explanation: Between 11 O’clock and 1 O’clock the hands of a clock coincide only once. So, the correct answer is (b).
(a) \[11:15\] pm (b) 11 pm
(c) 12 pm (d) \[12:30\] pm
(e) None of these
Ans. (b)
Explanation: Time from 5 am of a particular day to 10 pm on the 4th day is 89 hours. Now, the clock loses 16 minutes in 24 hrs or in other words we can say that 23 hours 44 minutes of this clock is equal to 24 hour of the correct clock.
or \[\left( 23+\frac{44}{60}=\frac{356}{15} \right)\] hours of this clock = 24 hours of the correct clock.
\[\Rightarrow \] 89 hours of this clock \[=\,\,\left( \frac{24\times 15}{356}\times 89 \right)\] hours of correct clock.
= 90 hours of the correct clock.
Therefore, it is clear that in 89 hours this clock loses 1 hour and hence the correct time is 11 pm when this clock shows 10 pm.
(a) 45 minutes past 4 (b) 40 minutes past 4
(c) \[50\frac{4}{11}\] minutes past 4 (d) \[54\frac{6}{11}\] minutes past 4
Ans. (d)
Explanation: At 4 O’clock both the hands are 20 minutes spaces apart and for having in the opposite direction they have to be 30 minute spaces apart.
From figure (i) and figure (ii) it is clear, that minute hand has to travel \[\left( 20+30 \right)\] minute spaces in order to be in opposite direction to each other. Now 55 minute spaces is gained in 60 minutes.
Therefore, 50 minute spaces will be gained in \[\left( \frac{60}{55}\times 60 \right)\] minutes or \[54\frac{6}{11}\] minutes.
Hence, the hands of the clock will be in opposite direction at \[54\frac{6}{11}\] minutes past 4.
Therefore, (d) is the correct answer.
(a) 7 hrs 30.18 minute (b) 7 hrs 35.18 minute
(c) 7 hrs 38.18 minute (d) 7 hrs 25.18 minute
(e) None of these
Ans. (c)
Explanation: At 7 am, the minute hand is 35 minute spaces behind the hour hand 55 minute spaces are gained in 60 minute
So 35 minute spaces will be gained in 38.18 minute.
Calendar
Days in a Week
There are seven days in a week - Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday.
If today is Monday then,
Example
(a) Tomorrow (b) Today
(c) Day after tomorrow (d) Two days after today
(e) None of these
Ans. (a)
Explanation: If day before yesterday was Thursday, then today is Saturday - Therefore tomorrow will be Sunday.
(a) Tuesday (b) Thursday
(c) Friday (d) Saturday
(e) None of these
Ans. (d)
Explanation: Clearly, nine days ago, it was Thursday. Therefore today is Saturday.
(a) Sunday (b) Monday
(c) Wednesday (d) Friday
(e) None of these
Ans. (c)
Explanation: Every day of the week is repeated after 7 days. Hence it will be Wednesday, after 98 days.
(a) Sunday (b) Monday
(c) Wednesday (d) Friday
(e) None of these
Ans. (c)
Clearly, 1st, 8th, 15th, 22nd and 29th of October are Sundays. So, 31st October is Tuesday. Therefore, 1st November will be Wednesday.
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