Question

the sum of digits of a two digit no. is 9. if the digits are interchanged the no. obtained exceeds the original no. by 27. find the no

Answer 1

HEY FRIEND
Let the two digit no. be 10x+y
Given x+y =9 , y=9-x
The no. formed after interchanging the digit is 10y+x
Then according to ques
10x+y+27=10y+x
then,
10x+9-x+27=10(9-x)+x
10x-x+9+27=10x+x
9x+36=90-36
18x=54
x=54/18
x=3

•• y = 9-3 = 6
No. is 10x+y
10×3+6
36

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Answer 2

Let the 10s place digit be x

Let the 1s place digit be y.

A.T.P

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

Original number =10x+y

New number after interchanging the digits=10y+x

A.T.P

(10y+x)-(10x+y)=27

-9x+9y=27

-9(x-y)=27

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

Adding (i) and (ii)

2x=6

x=3

Putting value of x in(i)

3+y=9

y=9-3

y=6

the original number:

10x+y=3*10+6=30+6=36(answer)