Question

The sum of the digits of a two-digit number is 12. If the digits are interchanged, the number is increased by 36. Find the number.

Answer 1

Answer:

48

Step-by-step explanation:

Let the number be 10x+y.

Given,

x + y = 12 ----------(1)

Also given,

10y + x = 10x + y + 36

10y - y = 10x - x + 36

9y = 9x + 36

9y = 9(x+4)

y = x+4

y - x = 4 or x - y = -4 --------------(2)

(1) + (2) gives,

2x = 12 - 4 = 8

x = 4

Substituting x = 4 in (1),

4 + y = 12

That is, y = 8

So, the original number is,

10x+y = 10x4 + 8 = 48.