Question

The sum of the digits of a two-dimensional no is 15.the no obtained by interchanging the exceeds the given no by 9.find the no

Answer 1

let unit's place digit is x.
Ten's place digit is y.
The required number will be 10y+x.

Number obtained after interchaning digits will be 10x+y.

by 1st condition
x + y = 15. ...... eq 1.

by 2nd condition,
10x+y > 10y + x by 9.
10x + y = 10y + x + 9
10x - x + y - 10y = 9
9x - 9y = 9
x - y = 1 dividing by 9 on both sides.
....... eq 2.
adding eq 1 and eq 2,
we get,
2x = 16
x = 8. put in eq 1
we get y = 7.

hence 10y + x = 10(7)+8 = 78.
hence the required number is 78