Question

the sum of digit of a 2- number is 8.the number obtained by interchanging the digit excedes the given number by 18. find the given number.

Answer 1

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original no is 35 and new number is 55

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Answer 2

Let tens place digit be x and units place digit be y.
So the given number is 10x+y.
By given condition,
x+y=8. …(1)

Number obtained by interchanging the digits is,
10y+x
By condition,
10y+x=10x+y+18
9x-9y+18=0
x-y=-2 ...(2)

Adding (1) and (2),we get
2x=6
x=3

Now putting x=3 in eqn(2),
3-y=-2
y=3+2
y=5

Hence the number is 10×3+5=35.