Question

sum of the digits of a two digits number is 9. when we interchange the digits, it is found that the resulting new number is greater than the original number by 27. what is the two digits number ​

Answer 1

Hi there!!!

Solution:

let the units digit be x and the tens digit be y.

hence,

the number =10x+y

now,

x+y= 9......(1)

also,

10x+y+27= 10y+x

10x+x+y-10y= -27

9x-9y= -27

9x-9y=-27

Dividing by 9,

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

now,

subtracting(2) from (1),

x+y= 9

- x+y= +3

2y = 12

y=12/2= 6

substituting value of x in (1),

x+y= 9

x+6= 9

x= 9-6

x= 3

hence,

the number= 10x+y= 6+10×3=

6+ 30= 36

Checking:

when the digits are interchanged,

the new number is greater than original by 27

36 when interchanged= 63

and 63= 36+27

hope this helps!! ❤✌☺

Answer 2

Answer:

digits in the tens place (*10) : 9-y and y

digits in the ones place (*1) : y and 9-y

sum of the digits : 9

number formed : (old number) 10(9-y)+y=90-10y+y=90-9y                                                                    (new number) 10y+9-y=9y+9

The equation is: new number=original number+27

                                         9y+9=90-9y+27

                                          9y+9y=90+27-9

                                           27y=108

                                           y=108/27=4

Original number is 90-9*7

                               =90-27=36

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