A number consists of two digits whose sum is 7. If 27 is added to the number , the digits are reversed. Find the number.

Let us assume that one of the digit of the two digit number is X, then problem the other number will be (7 - X)

From problem we get that, if we add 27 to the number the digits get interchanged and also since the number is a two digit number then X will in tens place & (7 - X) will be in ones place.

So the equation we get 

10X  + (7 - X) + 27 = 10(7 - X) + X

10X + 7 - X + 27 = 70 -10X + X

9X + 34 = 70 - 9X

9X + 9X = 70 - 34

18X = 36

X = 36/18

X = 2,

So the digit in tens plsce = 2 & the digit in ones place is (7 - 2 = 5) 5, then the number is 25 and when 27 is added the result is 52, the digits interchange their position in the new number.

Ans: 25.