Question

the ratio of a tens digit to the unit digit of a two digit number is 2:3. if 27 is addes to the number, the digits interchange their places, find the number

Answer 1

The ratio of tens digit =2:3
therefore x:y =2:3
3x=2y
-3x-2y= 0 (equation 1)
if 27 is added to the number ,so
10x +y+27=10y+x
9x-9y=-27
x-y=-3(equation 2 )
taking equation 1 and 2= 1 (3x-2y)= 0
3(x-y=-3)
3x-2y=0
3x-3y=-9
substracting 3x-3y=-9 from 3x-2y=0
3x-2y=0
-3x+3y=9 so Y=9
x-9=-3 soX=6
the number= 10(6)+9 =69

Answer 2

Hey

Here is your ,

Let the two digit number be 10x + y
The ratio of the tens digit to units digits = 2:3
Therefore
x:y = 2:3
3x = 2y
3x - 2y = 0 (Equation 1)

If 27 is added to the number, the digits interchange their places.
So,
10x + y + 27 = 10y + x
9x - 9y = - 27
x - y = - 3 (Equation 2).

Taking equation 1 and 2 as simultaneous equation
1(3x - 2y = 0)
3 (x - y = - 3)

3x - 2y = 0
3x - 3y = - 9

Subtracting 3x - 3y = - 9 from 3x - 2y = 0
3x - 2y = 0
- 3x + 3y = 9

y = 9

x - 9 = - 3
x = 6

The number is 10(6) + 9 = 69

Hope it helps you!