Question

The average of the two digit numbers, which remain the same when the digits interchange their position is:
A.33
B.44
C.55
D.66

Answer 1

Hint: Two-digit numbers which remain the same are the ones which have the same number on tens as well as unit places such as 11, 22, 33, etc. To find their mean, we will have to find the sum of all such numbers up to 99 and then divide by 9, which is the total number of values added.

Complete step-by-step answer:
The two-digit numbers which remain the same when the digits are interchanged are 11, 22, 33, 44, 55, 66, 77, 88 and 99.
The sum of these numbers will be given as \[11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495\].
Thus, their mean can be found out by dividing their sum by 9 which is the number of values added.
Thus, the mean of these numbers will be \[\dfrac{{495}}{9} = 55\].
Hence, option (C) is the correct option.

Note: It is important to find out which numbers is the question referring about. Another way of solving this could be that as there are 9 values, when we form a pair of two appropriate numbers they all add up to give 110 and thus their average will be 55. That is when we take the average of 11 and 99, we get 55, when we take 22 and 88 we get 55. Similarly we get the average of all such pairs as 55, so the average of these numbers will also be 55.