Question

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

Answer 1

$\tt\bf\red{Answer}$

Let the smaller number be x and the greater number be y.

Two digit number = 10x + y

According to 1st condition,

•°• sum of two digit number,

x + y = 7 ----> 1

According to 2nd condition,

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

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

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

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

19x - 8y = - 2 ----> 2

Multiply equation 1 by 8

8x + 8y = 56 ----> 3

Add equation 2 to 3,

19x - 8y = -2

8x + 8y = 56

----------------

27x = 54

x = $\bf\huge\frac{\cancel{54}}{\cancel{27}}$

$\bf\huge\boxed<strong> </strong>{<strong>x </strong><strong>=</strong><strong> </strong><strong>2</strong>}$

Substitute x = 2 in equation 3

8 (2) + 8y = 56

16 + 8y = 56

8y = 56 - 16

8y = 40

y = $\bf\huge\frac{\cancel{40}}{\cancel{8}}$

$\bf\huge\boxed<strong> </strong>{<strong>y </strong><strong>=</strong><strong> </strong><strong>5</strong>}$

•°• x = 2 & y = 5

The two digit number so formed is $\bf\boxed {25}$