If a clock strikes once at one O'clock twice at two O'clock ,thrice at 3 O'clock and so on , and again once at one O'clock and so on , then how many times will the bell be struck in the course of 2 days ?

Options

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

Answer

To solve the problem of how many times the clock strikes in the course of 2 days, we can break it down step by step.

### Step 1: Understand the striking pattern
The clock strikes as follows:
- At 1 O'clock: 1 strike
- At 2 O'clock: 2 strikes
- At 3 O'clock: 3 strikes
- ...
- At 12 O'clock: 12 strikes

### Step 2: Calculate the total strikes in 12 hours
To find the total number of strikes in a 12-hour period, we need to sum the strikes from 1 O'clock to 12 O'clock:
\[ \text{Total strikes in 12 hours} = 1 + 2 + 3 + ... + 12 \]

This is an arithmetic series where:
- The first term \( a = 1 \)
- The last term \( l = 12 \)
- The number of terms \( n = 12 \)

The formula for the sum of the first \( n \) natural numbers is:
\[ S_n = \frac{n(n + 1)}{2} \]

Substituting \( n = 12 \):
\[ S_{12} = \frac{12(12 + 1)}{2} = \frac{12 \times 13}{2} = \frac{156}{2} = 78 \]

### Step 3: Calculate the total strikes in 24 hours (2 days)
Since the clock strikes 78 times in 12 hours, in 24 hours (which is 2 days), the total strikes will be:
\[ \text{Total strikes in 24 hours} = 78 \times 2 = 156 \]

### Conclusion
Thus, the total number of times the bell will be struck in the course of 2 days is **156**.

---