NIELIT 2019 Feb Scientist C - Section D: 20

Question

If a clock strikes once at one o’clock, twice at two o’clock and twelve times at $12$ o’clock and again once at one o’clock and so on, How many times will the bell be struck in the course of $2$ days?

• A. $156$
• B. $312$
• C. $78$
• D. $288$

Answer 1

Answer is B. 

In a day, clock ticks 12’O clock 2 times. In 2 days, clock with strike 12’o clock 4 times.

So, a clock strikes once at one o’clock, twice at two o’clock and twelve times at 12 o’clock, this means (1 + 2 + 3 + … + 11 + 12).

(1 + 2 + 3 + … + 11 + 12) is sum of 12 terms which is in AP. So, sum of the first n terms in an arithmetic sequence is (n/2)⋅(a₁+aₙ). 

Here sum = (12/2)*(1+12) = 78

for 2 days, no:of times clock will strikes is 4 * (1 + 2 + 3 + … + 11 + 12) = 4*78 = 312