Question

a number has two digits whose sum is 9 if 27 is added to the number its digits get interchanged find the number?

Answer 1

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Let the digit at ones place = x 

digit at tens place = 9 - x 

original number = 10 ( 9 - x) + x = 90 - 9x   to (1) 

When the digits are reversed, then new number = 10x + (9 - x) = 9x + 9 

according to the given condition, 

(90 - 9x) - (9x + 9) =  27  

- 9x - 9x = 9 + 27 - 90 

- 18x = - 54 ⇒ x = 3 

so from (1), we get 

original number = 90 - 9 × 3 = 90 - 27 = 63

Answer 2

Let the number be 10x+y.
x+y = 9 EQUATION NO. 1
10x+y +27 = 10y+x.
simplifying this further
9x -9y +27 = 0
x - y = -3 EQUATION NO.2
Adding 1st and 2nd equation gives,
2x = 6
x =3.
Substituting x =3 in 1st equation
3 +y =9
y =6

Thus the required no. is 10(3) +6 = 36