Question

in a no of twodigits the sum of the digit is 7.if 27is added to the no.theno.is reversed .find the no.

Answer 1

let the digit in the units place be x
their sum is 7
therefore, digit in the tens place=7-x
the number is
10(7-x)+x
=70-10x+x
=70-9x______(i)

given,
if 27 is added to the number,the digits are reversed.

therefore,

digits in units place = 7-x
digit in tens place=x
the new number is
10(x)+7-x
10x+7-x
=9x+7_____(ii)

according to the question,

70-9x+27=9x+7
97-9x=9x+7
97-7=9x+9x
90=18x
$x = \frac{90}{18}$
x=5

digit in units place=x=5
digit in tens place=7-x=7-5=2

the original number is 25