What is the 10′ complement of (47)₅₂?

The correct option is 53.

To find the 10's complement of a decimal number, we can use two common methods: the direct formula method or the subtraction-from-9's-complement method.

Method 1: Direct Formula
The $r$'s complement of an $n$-digit number $N$ in base $r$ is given by the formula:
$r^n-N$
Here, the base is decimal ($r=10$) and the number is 47, which has $n=2$ digits. Substituting these values into the formula:
${10}^2-47=100-47=53$

Method 2: Using the 9's Complement
Alternatively, the 10's complement can be calculated by first finding the 9's complement of the number and then adding 1 to the result.
1. Find the 9's complement of 47 by subtracting each digit from 9:
$99-47=52$
Note: The subscript 52 in the question refers to this intermediate 9's complement of the number 47.
2. Add 1 to the 9's complement to obtain the 10's complement:
$52+1=53$

Both methods yield the same result, confirming that the 10's complement of 47 is 53.