Question

The sum of the digits of a two digit number is 12. the number obtained by reserving the digits is 36 greater than the original number. Find the number. ​

Answer 1

Answer:

• Sum of the digits of a two digit number = 12
• On reversing the number the new number is 36

Asume the numbers to be 10x+y and on reversing they become 10y+x

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• The sum of the digits give us 12

$\displaystyle\sf :\implies x+y = 12\:\:\:-eq(1)$

• When the digits are reversed we get a new Number that's 36 more than the original number

$\displaystyle\sf :\implies 10y+x = 10x+y+36$

$\displaystyle\sf :\implies 10y+x-10x-y = -36$

$\displaystyle\sf :\implies -9x+9y = 36$

$\displaystyle\sf :\implies 9x-9y = 36$

[Dividing the whole equation by 9]

$\displaystyle\sf :\implies \dfrac{9x}{9}-\dfrac{9y}{9} = \dfrac{36}{9}$

$\displaystyle\sf :\implies x-y = 4\:\:\: -eq(2)$

Subtracting eq(2) from eq(1)

$\displaystyle\sf :\implies 2y = 8$

$\displaystyle\sf :\implies y = \dfrac{8}{2}$

$\displaystyle\sf :\implies\underline{\boxed{\sf y = 4}}$

Now the value of x will be,

$\displaystyle\sf :\implies x+y = 12$

$\displaystyle\sf :\implies x+4 = 12$

$\displaystyle\sf :\implies x = 12-4$

$\displaystyle\sf :\implies\underline{\boxed{\sf x = 8}}$

$\displaystyle\underline{\bigstar\:\textsf{The Original number :}}$

$\displaystyle\sf \dashrightarrow 10x+y$

$\displaystyle\sf \dashrightarrow 10\times 8+4$

$\displaystyle\sf \dashrightarrow 80+4$

$\displaystyle\sf \dashrightarrow \textsf{\textbf{Original Number = 84}}$