The average of the two digit numbers, which remain the same when the digits interchange their positions is :
Solution
Two digit numbers which remain same after interchanging the digits = 11,22,33,....,99
The above expression is an A.P with first term, $$a = 11$$ and common difference, $$d = 11$$
Number of terms = 9
Sum of A.P. = $$\frac{n}{2} (a + a_n)$$
= $$\frac{9}{2} (11 + 99) = \frac{9}{2} \times 110$$
= $$9 \times 55$$
$$\therefore$$ Required average = $$\frac{9 \times 55}{9} = 55$$
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