Question

le 4. A number consists of two digits whose sum is 6. If 18 is added to the number, its digits are reversed.
Find the number


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Answer 1

Let the ten's digit and the one's digit be x and y respectively.

Given

Sum of the digits = 6

$\implies x+y=6--(1)$

If 18 is added to the number, its digits are reversed.

$\implies 10x+y+18=10y+x\\\implies 10x-x+y-10y=-18\\\implies 9x-9y=-18\\\implies x-y=-2--(2)$

Solving (1) and (2), we get,

$x+y=6\\\underline{x-y=-2}\\\underline{\underline{\\2x=4}}\\\implies x = 2$

$\implies y = 4$

$\boxed{\boxed{\bold{Therefore, \ the \ number \ is \ 24}}}}}$