The correct answer is (b).
The average of five numbers is 10, so the sum of the five numbers is $5 \times 10 = 50$. If we add $x$ to the five numbers, the new sum will be $50 + x$. The new average will be $12$, so we have the equation $50 + x = 5 \times 12 = 60$. Solving for $x$, we get $x = 60 – 50 = 10$. Therefore, the number that should be added to make the average 12 is 10.
Option (a) is incorrect because 12 is already the average of the five numbers. Adding 12 to the five numbers will not change the average.
Option (c) is incorrect because 22 is greater than the average of the five numbers. Adding 22 to the five numbers will increase the average.
Option (d) is incorrect because 24 is also greater than the average of the five numbers. Adding 24 to the five numbers will also increase the average.