Question

The sum of digits of a 2 digit number is 7. if 27 is added to the number, the digits interchange their places. find the number.

Answer 1

25 is answer
2+5=7
And 25+27=52

Answer 2

Hey mate!!!!

Let first digit be x
second be y
When we write then as 2 digit number, we write as 10x +y.

Given x +y = 7
and
10x + y +27 = 10y +x (because they interchange digits)

so we have
$10x + y + 27 = 10y + x \\ 10x + y - 10y - x = - 27 \\ 9x - 9y = - 27 \\ 9(x - y) = - 27 \\ x - y = - 27 \div 9 \\ x - y = - 3$
now we know x - y = -3
we are given x + y = 7
adding them we have
$x + y + x - y = 7 - 3 \\ 2x = 4\\ x = 4\div 2 \\ x = 2$
now x is 2
so y =
$x + y = 7 \\2+ y = 7 \\ y = 7 - 2\\ y = 5$
now the number is
$10x + y \\ = > 10 \times 2 + 5\\ = > 25$
so the number is 25


Hope it helps dear friend ☺️✌️