A certain number of two digits is seven times the sum of its digits and if 27 be subtracted from it, its digits will be reversed. Find the number.

47

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29

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38

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63

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Solution

The correct option is C $63$
$L e t t h e o n e^{'} s d i g i t = x T e n^{'} s d i g i t = y N o = 10 y + x = 10 y + x = 7 (x + y) 10 y + x = 7 x + 7 y 3 y = 6 x o r y = 2 x => e q n 1 10 y + x - 27 = 10 x + y 9 y - 9 x = 27 y - x = 3 => e q n 2 S u b 1 i n 2 x = 3 y = 3 + x = 6 N o = 63$

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