Question

sum of digit of a two digit no. whose 9.when we interchange the digit a new no. is greater than the original no by 27.what is the two digit no.

Answer 1

let the 1st digit be x

2nd digit be y

according to the question,

x+y=9 -------- 1

the original no is 10x +y

on interchanging the digits the no becomes 10y+x

according to the question ,

10y+x=10x+y+27

10y-y+x-10x=27

9y-9x=27

9(y-x)= 27

y-x=27/9

y-x= 3

-x+y= 3 -------- 2

now we can solve equation 1 and 2 using elimination method ,

on adding eq 1 and 2 we get,

x+y=9

+ (-x+y=3)

__________

2y = 12

y= 12/2

y=6

now substitute the value of y in eq 1 ,

x+y=9

x+6=9

x=9-6

x=3

hence,

first digit of the no = x = 3

2nd digit of the no= y = 6

hence , your no is 36

hope my answer helps you :)