Question 22

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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