A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then `k-20` is equal to

Explanation

To solve the problem, we need to find the value of \( k - 20 \) given that two consecutive numbered cards are removed from a pack of \( n \) cards numbered from 1 to \( n \) and the sum of the remaining cards is 1224.

### Step-by-step Solution:

1. **Calculate the sum of the first \( n \) natural numbers**:
The sum of the first \( n \) natural numbers is given by the formula:
\[
S_n = \frac{n(n + 1)}{2}
...