If a clock strikes appropriate number of times at each hour, how many times will it strike a day ?

Options

A. 300
B. 156
C. 68
D. 78

Answer

To find out how many times a clock strikes in a day, we can break down the problem step by step.

### Step 1: Understand the striking pattern
A clock strikes the following number of times at each hour:
- 1 time at 1 o'clock
- 2 times at 2 o'clock
- 3 times at 3 o'clock
- ...
- 12 times at 12 o'clock

### Step 2: Calculate the total strikes in 12 hours
We need to find the total number of strikes from 1 o'clock to 12 o'clock. This can be calculated using the formula for the sum of the first n natural numbers, which is given by:

\[ \text{Sum} = \frac{n(n + 1)}{2} \]

In this case, \( n = 12 \).

### Step 3: Apply the formula
Substituting \( n = 12 \) into the formula:

\[ \text{Sum} = \frac{12(12 + 1)}{2} = \frac{12 \times 13}{2} \]

### Step 4: Simplify the calculation
Calculating the multiplication:

\[ 12 \times 13 = 156 \]

Now divide by 2:

\[ \frac{156}{2} = 78 \]

So, in 12 hours, the clock strikes a total of 78 times.

### Step 5: Calculate the total strikes in a day
Since a day consists of two 12-hour periods (AM and PM), we multiply the total strikes in 12 hours by 2:

\[ \text{Total strikes in a day} = 78 \times 2 = 156 \]

### Final Answer
Thus, the clock will strike a total of **156 times in a day**.

---