Question

10. The sum of the digits of a two-digit number is 13. If 27 is added to the
number, the digits get interchanged. What is the number?
(1) 58
(2) 85 (3) 49 (4) 94​

Answer 1

$\huge \star \: { \boxed{ \underline{ \mathfrak{ \purple{Answer}}}}}$

Let two digit no. x and y

Given

x+y=13−−−(1)

xy+27=yx−−−(2)

⇒ 10x+y+27=10y+x

9x+27=9y

x+3=y−−−−−(3)

Adding (1) and (2)

2x=10

⇒ y=13−5=8

⇒  Number is 58