Question

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

Answer 1

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 this helps you.

Answer 2

Answer:

answer is 69...........