Question

Sum of digits of a two digit no. is 9. if 45 is added to the number, the digits are interchanged. find the number​

Answer 1

Let the digit at ones place be 'x '

▪Let the digit at tens place be 'y'

♦Number formed => x + 10 y .....................(1)


➰According to the given question:
===============================

x + y = 9

y = 9 - x .......................(2)


x + 10 y + 45 = 10x + y

-9x + 9y + 45 = 0


From (2)

-9x + 9 ( 9 - x ) + 45 = 0

-9x + 81 - 9x + 45 = 0

-18x + 126 = 0

-18x = -126

=> x = 7
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From (2)

y = 9 - 7

y = 2
=====


▪◾Number is x + 10y

=>> 7 + 10(2)

=>> 7 + 20

=> 27

Answer 2

Answer:

27

Step-by-step explanation:

Let original number in the form xy

              or,  10x + y

Interchanged number will be yx

               or, 10y + x  

Given ,  x + y = 9                                                                        .......(a)  

Now , ( 10x + y )  + 45  =  10y + x

           10x - x + y - 10y  =  -45

                 9x - 9y  =  -45

                9( x - y )  =  -45

                     x - y    =  -45 / 9

                      x - y    =   -5                                                           .......(b)

  solving  (a) and (b) or adding (a) and (b) ......

        2x  =  4

           x  =  2

putting value of x in (a) or (b) .....

        y = 7

original number  =  10x  +  y  =  10(2) + 7   =  20  + 7  =  27

                             

                                                                                                        thanks