A number consist of two digits. If the digits interchange their places and the new number is added to the original number becomes two times of the original number. Find the number.

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Solution

$L e t t h e n u m b e r b e " a b " t h e n (10 b + a) + (10 a + b) = 2 (10 a + b) 10 b + a = 10 a + b o r 9 b = 9 a ∴ a = b ∴ n u m b e r s l i k e 11, 22, 33, 44, 55, 66, 88, 99, 77 w i l l s a t i s f y t h i s c o n d i t i o n$

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A number consist of two digits. If the digits interchange their places and the new number is added to the original number becomes two times of the original number. Find the number.

Letthenumberbe"ab"then(10b+a)+(10a+b)=2(10a+b)10b+a=10a+bor9b=9a∴a=b∴numberslike11,22,33,44,55,66,88,99,77willsatisfythiscondition

$L e t t h e n u m b e r b e " a b " t h e n (10 b + a) + (10 a + b) = 2 (10 a + b) 10 b + a = 10 a + b o r 9 b = 9 a ∴ a = b ∴ n u m b e r s l i k e 11, 22, 33, 44, 55, 66, 88, 99, 77 w i l l s a t i s f y t h i s c o n d i t i o n$