The sum of all the digits of the number $({10}^{50}+{10}^{25}-123)$, is

The correct option is 221.

To find the sum of all the digits of the number, let us first analyze and simplify the given expression:
$({10}^{50}+{10}^{25}-123)$
We can write this expression by grouping the terms as:
${10}^{50}+({10}^{25}-123)$

Step 1: Simplify the term ${10}^{25}-123$
The number ${10}^{25}$ consists of a 1 followed by 25 zeros, representing a 26-digit number.
When we subtract 123 from ${10}^{25}$, the last few digits are determined by:
$1000-123=877$
All the remaining digits to the left of 877 turn into 9s. Since ${10}^{25}$ has 25 zeros, the subtraction results in a 25-digit number:
${10}^{25}-123=\underset{⏟\text{22 times}}{999\dots 999}877$
Thus, the number ${10}^{25}-123$ consists of:
• Twenty-two 9s
• One 8
• Two 7s

Step 2: Add ${10}^{50}$ to the result
The number ${10}^{50}$ is a 1 followed by 50 zeros.
When we add ${10}^{50}$ to $({10}^{25}-123)$, the 25-digit number from Step 1 occupies the lowest 25 place values. The digit 1 from ${10}^{50}$ is at the 51st position, and all intermediate positions (from the 26th to the 50th position) are filled with zeros.
Therefore, the combined number has the following digits:
• One 1 (at the most significant position)
• 24 zeros
• Twenty-two 9s
• One 8
• Two 7s

Step 3: Calculate the sum of all the digits
Now, we sum the individual digits of the resulting number:
$\text{Sum of digits}=1+(24\times 0)+(22\times 9)+8+7+7$
Let us compute the sum step-by-step:
$\text{Sum of digits}=1+0+198+8+7+7$
$\text{Sum of digits}=199+22=221$