Question

the sum of the digits of a two digit number is 7.The number obtained by interchanging the digitdexceeds 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)+x70 x -10 x +x70 x -9x
when the digits are interchanged than
,t's digit= xu'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)=279
 x + 7 - 70 + 9x =2718
x -63= 2718
x = 63+2718
 x= 90x
= 90/18=5
the no. = 70- 9x 
=> 70-45
=> 25
ans
verify : 2+5 = 7

Answer 2

The answer can be 25as 2 + 5=7,if we interchange the numbers it will be 52.The difference in 27 between 52 and 25.So the answer is 25