Question

If a clock strikes once at 1'o clock, twice at 2'o clock, thrice at 3'o clock, and so on, how many times will it strike in a day?
(Assume that the clock strike at 12 midnight is also counted.)

• A. 124
• B. 156
• C. 204
• D. 78

Answer 1

The correct option is B 156

The clock strikes once at 1'o clock, twice at 2'o clock, and so on.

We need to find out the sum of the terms in both the sequences.

Time	1	2	3	4	5	6	7	8	9	10	11	12
Number of strikes	1	2	3	4	5	6	7	8	9	10	11	12

The given sequence is an arithmetic sequence, which increases by one every hour.

Sum = 1 + 2 + .......... + 12 (i)

Even if the order of the sequence is reversed, the sum will remain the same.
Sum = 12 + 11 + .......... + 1 (ii)

Adding the two sum equations,
$2\times \text{Sum}=(1+12)+(2+11)+..........+(12+1)$

$\Rightarrow 2\times \text{Sum}=13+13+.......+(3+10)+(2+11)+(1+12)$

$\Rightarrow 2\times \text{Sum}=13(1+1+.....12\text{times})$
$\Rightarrow 2\times \text{Sum}=13\left(12\right)$
$\Rightarrow 2\times \text{Sum}=156$
$\Rightarrow \text{Sum}=\frac{156}{2}=78$

So, in 12 hours the bell will strike 78 times.

Hence, in the whole day the number of strikes will be
$=2\times 78$
$=156$