Question

Sum of two digit number is 9.when we interchange the digits it is found that the resulting new number is greater than the original number by 27what is the two digit number

Answer 1

Answer:

36

Step-by-step explanation:

let the digits be x and y

so, the number = (10x + y) and the no after interchanging digits = (10y+x)

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

      10y + x - (10x + y) = 27

or ,  10y + x - 10x -y =27

or   9y - 9x =27

or   9(y-x) = 27

or   y-x = 3....(ii)

adding (i) and (ii),

y+x+y-x = 9+3 =12

or,2y = 12 or, y=6 and x=3

the number is 36

Answer 2

Answer:

let the number be 10 a +b

according to question a+b=

b=9-a

now after interchanging the digit

10b+a=10a+b+27

10b-b=10a-a+27

9b=9a+27

put b=9-a,we get

9(9-a)=9a+27

taking 9 as common we get

9-a=a+3

2a=6

a=3

b=9-a

b=9-3

b=6

the number is 36