Question

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.

Answer 1

Let the digit at unit’s place be x and the digit at ten’s place be y.
Required no. = 10y + x
If the digit’s are reversed
Reversed no. = 10x + y

According to the question,

x + y = 7                        ...(1)

and,

10x + y - 2 = 2(10y + x)

10x + y - 2 = (20y + 2x)

8x - 19y = 2                  ...(2)

Multiplying equation no. (1) by 19.

19x + 19y = 133           ...(3)

Now adding equation(2) and (3)
       19x + 19y = 133                
 +      8x - 19y = 2     
                 27x = 135

`x = 135/27`

x = 5

From (1)

5 + y = 7

y = 7 - 5

y = 2

Required number is = 10(2) + 5 = 25.