Question

Sum of the digits of a two number is 5. When the digits are reversed, the resulting number is greater than the original number by 27. Find the
number.
Please step by step explanation. ​

Answer 1

let the tens digit be x

and the unit digit be y

so according to question:

x+y= 5...............(1)

10y+x= 10x+y+27

9y=9x+27

Or y-x= 3.............(2)

adding equation (1) and (2)

y= 4 and x=1

so the number will be 14

Answer 2

Let,

• Digit in the units place be y

• Digit in the tens place be x.

Hence,

Original number = 10x + y  → (1)

x + y = 5

⇒ y = 5 - x  → (2)

$\implies 10y + x = 10x + y + 27$

$\implies 10y - y = 10x - x + 27$

$\implies9y=9x+27$

Divide throughout by 9

$\implies y=x+27$

From (2),

$\implies 5-x=x+27$

$\implies 2x=-22$

$\implies x=-11$

Substituting the  value of x in (2)

$\implies y=5-(-11)$

$\implies y = 5+11$

$\implies y = 16$

Substituting the value of x and y in (1)

$Original \:Number=10(-11)+16$

$\implies Original\:Number =-110+16$

$\implies Original \:Number =-94$

Hence,

$\boxed{\bold{Original \: Number = -94}}$