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 tens digit be x,
and the unit digit be y.

Then, according to question,
Tens digit = 2x
Unit digit = 3y

Then the number is :
=> 10x + y

And,
=> ( 10x + y ) + 27 = 10y + x
=> 9x - 9y = 27
=> 2( x - y) = (3 × 2)
=> 2x - 2y = 6 .............(i)

Also, 2x = 3y
=> 2x - 3y = 0 .............(ii)

By elimination method:

Using equation (I) & (ii),
=> 2x - 2y - (2x - 3y) = 6
=> y = 6

From equation (ii),
=> 2x - 3y = 0
=> 2x -18 = 0
=> x = 9

So, the number is 10x + y
=> 90 + 6
=> 96