Question

the sum of the digits of a two digit number is 7. the number obtained by interchanging digits exceeds the original number by 27 find the number.

Answer 1

let the units place be x
then the tens digit be 7 - x
number formed by these digits = 10 x t's digit+u's digit
=> 10(7-x)+x
70 x -10 x +x
70 x -9x
when the digits are interchanged than,
t's digit= x
u's digit = 7-x
the new no. formed = 10x + 7-x
= 9 x +7
given that the no. exceeds by 27
new no. - given no.
9x +7 - (70-9x)=27
9 x + 7 - 70 + 9x =27
18x -63= 27
18 x = 63+27
18 x= 90
x = 90/18
=5
the no. = 70- 9x 
=> 70-45
=> 25 ans
verify : 2+5 = 7

Answer 2

Let the first digit = x
Therefore second digit = 7-x
Number = 10×(7-x)+1×x
= 70-10x+x
= 70-9x

On interchanging the digits, number becomes= 10×x+1×(7-x)
= 9+7x

ATQ
9+7x-(70-9x)=27
9+7x-70+9x=27
18x-63=27
18x = 27+63
X = 2

Therefore first digit= 2

Number = 10×2+1×5
= 25

Hope this helps you!:)