Question

a clock strikes once at 1 o'clock twice at 2 o' clock and thrice at 3 o' clock and so on. if vit takes 12 seconds to strike at 7 o' clock. find the time taken by it to strike at 11 o' clock​

Answer 1

Step-by-step explanation:

There are 24 hours in a day and clock has 12 hours, therefore, there will be two rounds of clock per day. Let us write this as an arithmetic series because we have to find the number of times that the clock strike in a day. Thus, the A.P is

1,2,3,4,....,12

We know that the sum of an arithmetic series with first term a and common difference d is S

n

=

2

n

[2a+(n−1)d]

Now to find the sum of series, substitute n=12,a=1 and d=2−1=1 in S

n

=

2

n

[2a+(n−1)d] as follows:

S

12

=

2

12

[(2×1)+(12−1)1]=6[2+(11×1)]=6(2+11)=6×13=78

Therefore, it will strike 78 times in 12 hours.

Now to find the number of times it will strike in full day that is in 24 hours is 2×78=156.

Hence, the clock strikes 156 times in a day.

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