The sum of digits of a two digit number is 9. If on adding 27 to the number, its digits reverse, find the number.

36

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10

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86

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49

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Solution

The correct option is A $36$
$L e t t h e o n e^{'} s d i g i t = x T h e S u m o f o n e^{'} s a n d t e n^{'} s d i g i t = 9 T e n^{'} s d i g i t = 9 - x N o = 10 (9 - x) + x N o . r e v e r s e d = 10 x + (9 - x) 10 (9 - x) + x + 27 = 10 x + 9 - x (a d d 27, d i g i t s g e t r e v e r s e d) 90 - 10 x + x + 27 = 9 x + 9 18 x = 108 x = 6 t e n s^{'} s d i g i t = 9 - 9 = 3 N o = 36$

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