Consider two-digit numbers which remain the same when the digits inter...
All such 2 digit numbers are 11,22,33,44……. upto 99
Forms an AP
So sum = n/2(a+l)
= 9/2(11+99)
Average = sum/9 = ½(11+99) = 55
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Consider two-digit numbers which remain the same when the digits inter...
To find the average of two-digit numbers that remain the same when the digits interchange their positions, we need to first list down all the possible numbers that satisfy this condition.
Two-digit numbers have a tens digit and a units digit. For the number to remain the same when the digits interchange their positions, the tens digit and the units digit should be the same.
Let's list down the numbers that satisfy this condition:
11 (tens digit = 1, units digit = 1)
22 (tens digit = 2, units digit = 2)
33 (tens digit = 3, units digit = 3)
44 (tens digit = 4, units digit = 4)
55 (tens digit = 5, units digit = 5)
66 (tens digit = 6, units digit = 6)
77 (tens digit = 7, units digit = 7)
88 (tens digit = 8, units digit = 8)
99 (tens digit = 9, units digit = 9)
There are 9 numbers in total that satisfy the given condition.
Now, to find the average of these numbers, we add them up and divide the sum by the total number of numbers.
Sum of all the numbers = 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 = 495
Total number of numbers = 9
Average = Sum of all the numbers / Total number of numbers = 495 / 9 = 55
Therefore, the average of two-digit numbers that remain the same when the digits interchange their positions is 55.
Hence, the correct answer is option C) 55.