The digits of 2 digit number differ by 5. If the digits are interchanged and the resulting number is added to their original number, then we get 99. find the original number
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let the digits be x and y
then x-y=5
the original no = 10x + y
and on interchanging no = 10y + x
now on their addition as per q, we get 11x +11y = 99 or x +y =9
solving the two equations we get x = 7 and y = 2
AND SO NO IS 72
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Answered by
1
let the one digit no. be x
another be x+5
The tens will be 10x
and once will be x+5
the interchanged no. will be 10(x+5) x
10(x+5)+x+10+(x+5)=99
=> 11(x+5)+11x=99
=> 11x+55+11x=99
=> 22x+55=99
=> 22x=99-55
=> x=44/22
=> x=2
so 1st digit =2
2nd digit = 2+5=7
original no. is 27
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