Question

The sum of digit of a two digit number is 9.
The digit are reversed when 9 is added to the number. Find the number.

Answer 1

Given :

• The sum of digit of a two digit number is 9.

• The digit are reversed when 9 is added to the number.

To find :

• The number =?

Step-by-step explanation :

Let, the ones digit of two digits number be, x.

Then, the tens digit of two digits number be, 9 - x.

So, the number will be, 10(9 - x) + x = 90 + 9x

After reversing the digits the number will be,

= 10x + (9 - x)

= 9x + 9.

According to the question :

➮ 90 - 9x = 9x + 9 - 9

➮ 18x = 90 - 9 + 9

➮ 18x = 90

➮ x = 90/18

➮ x = 5.

Hence,

Ones digit, x = 5

Ten's digit, 9 - x = 9 - 5 = 4

Therefore, the new number = 10 × 4 + 5 = 45

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\:\:$

$\green{\underline \bold{Given :}}$

$\:\:$

• Sum of digit of a two digit number is 9

$\:\:$

• Digit gets reversed when 9 is added to the number.

$\:\:$

$\red{\underline \bold{To \: Find:}}$

• The original number

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the tens digit be 'x'

Let the ones digit be 'y'

$\:\:$

$\underline{\bold{\texttt{Original number :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf 10x + y$

$\:\:$

$\underline{\bold{\texttt{Reversed number :}}}$

$\:\:$

$\purple\longrightarrow$ $\sf 10y + x$

$\:\:$

$\purple{\underline \bold{According \: to \: the \ question :}}$

$\:\:$

$\bf \dashrightarrow x + y = 9$ -------(1)

$\:\:$

Also,

$\:\:$

$\sf \longmapsto 10x + y + 9 = 10y + x$

$\:\:$

$\sf \longmapsto 10x - x + y - 10y = -9$

$\:\:$

$\sf \longmapsto 9x - 9y = -9$

$\:\:$

$\underline{\bold{\texttt{Dividing the above equation by 9}}}$

$\:\:$

$\bf \dashrightarrow x - y = -1$ -------(2)

$\:\:$

$\red{\bold{Equation \: (1) \: + \: Equation \: (2)}}$

$\:\:$

$\sf \longmapsto x + y + x - y = 9 - 1$

$\:\:$

$\sf \longmapsto 2x = 8$

$\:\:$

$\sf \longmapsto x = \dfrac { 8 } { 2 }$

$\:\:$

$\bf \dashrightarrow x = 4$ ------(3)

$\:\:$

$\underline{\bold{\texttt{Putting x = 4 in (1)}}}$

$\:\:$

$\sf \longmapsto 4 + y = 9$

$\:\:$

$\sf \longmapsto y = 9 - 4$

$\:\:$

$\bf \dashrightarrow y = 5$

$\:\:$

$\underline{\bold{\texttt{Original number :}}}$

$\:\:$

$\purple\longrightarrow$$\sf 10(4) + 5$

$\:\:$

i.e 45 is the original number

$\rule{200}5$