Question

the sum of a 2 digit number is 7. the number obtained by interchanging the digits exceeds the original number by 27. find the number

Answer 1

let the original number be 10x + y
sum of digits = x + y = 7                       ........(i)
after interchanging the digits, the no. becomes 10y + x

Now,
10y + x = 10x + y +27
⇒ 9y - 9x = 27
⇒ 9(y - x) = 27
⇒ y - x = 3
⇒ y = 3 + x                                     ..........(ii)

Substituting value of y = 3 +x in (i), we get
⇒ x + 3 + x = 7
⇒ 2x = 4
⇒ x = 2
∴ y = 5
⇒ 2-digit no. = 10x +y = 25