Question

Sum of the digits of a two-digit number is 9. When we interchange the digits it is found that the reasulting new number is greater than the original number by 27 what is the two digit number

Answer 1

Let the digits be x(ten's digit) and y(one's digit)

so the number is: 10x+y

Given,

x+y=9 ....(1)

and

10y+x-(10x+y)=27

9y-9x=27 ....(2)

Multiplying 9 to the both sides of eq. 1 we get,

9x+9y=81

now by solving eq. 1 and 2, we get.

9y-9x=27

9y+9x=81

__________

18y=108

y= 6

by putting the value of y in eq.1 we get,

x+6=9

x=3

so the original number was,

10x+y = 10*3+ 6= 30+6=36

that's it.

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