Question

A number consists of two digits whose sum is 8. If 18 is added to the number its digits are
reversed. Find the number.
​

Answer 1

Let one digit of the number be x , then its ten  digits digits will be (8−x) . 

So , given number =10(8−x)+x 

                                 =80−10x+x 

                              =80−9x

Now if digits are reversed  , then Number obtained  

                                 =10x+(8−x)

                                 =10x+8−x

                                 =9x+8

According to question 

        (80−9x)+18=9x+8

         98−9x=9x+8 

         90=18x

           x=5

⇒ given number  =80−9x

                                          =80−9×5      

                                          =80−45 

                                          =35         

                                        

∴ the number is 35

Answer 2

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

• Sum of digits of 2 digit no. is = 8
• If 18 is added to number its digit got reversed .

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Original number = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

Original number = 10 x + y

⠀⠀⠀⠀

• sum of digits is 8

⠀⠀⠀⠀

x + y = 8 ---- ( i )

⠀⠀

• If 18 is added to the number its digit got reversed

⠀⠀⠀⠀

Reversed no. = 10y + x

⠀⠀⠀⠀

10 x + y + 18 = 10y + x

⠀⠀⠀⠀

10y - y - 10x + x = 18

⠀⠀

9y - 9x = 18

⠀⠀

9 ( y - x ) = 18

⠀⠀⠀⠀

y - x = 18 / 9

⠀⠀⠀⠀

y - x = 2

⠀⠀⠀⠀

• Adding eq ( i ) and ( ii )

⠀⠀

x + y + y - x = 8 + 2

⠀⠀⠀⠀

2y = 10

⠀⠀⠀⠀

y = 10 / 2

⠀⠀⠀⠀

y = 5

⠀⠀⠀⠀

• putting value of y in eq ( i )

⠀⠀⠀⠀

x + y = 8

⠀⠀⠀⠀

x + 5 = 8

⠀⠀

x = 8 - 5

⠀⠀⠀⠀

x = 3

⠀⠀⠀⠀

• finding the number

⠀⠀

10x + y

⠀⠀⠀⠀

10 x 3 + 5

⠀⠀⠀⠀

30 + 5

⠀⠀

35

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Original number = 35