Question

The sum of the digits of a 2 digit number is 14. If the number formed by interchanging the digits exceeds the given number 36, what is the number.

Answer 1

Let the unit digit be x and ten digit be y,

So,

Number = 10x + y

According to the Question:

==> x + y = 14 ...(1)

Also,

Number formed by interchanging the digits exceeds the original number by 36,

==> 10x + y + 36 = 10y + x

==> 9x - 9y = -36

==> 9(x - y) = -36

==> x - y = -4 ...(2)

Solving (1) and (2),

==> x + y + x - y = 14 - 4

==> 2x = 10

==> x = 5

Putting value of x in (1)

==> x + y = 14

==> y = 14 - 5

==> y = 9

Number = 10x + y

==> 10(5) + 9

==> 50 + 9

==> 59

Hence, The number is 59