Question

What is the two-digit number?

I.

The difference between the two-digit number and the number formed by interchanging the digits is 27.

II.

The difference between the two digits is 3.

III.

The digit at unit's place is less than that at ten's place by 3.

Answer 1

3 and 0

Explanation:

Let's assume, the first digit (ten's place) is x and the second one (unit's place) is y

Let's write 2 equations according to the given information and put them in a system (we can write a 2 digit number as 10x + y, and after interchanging: 10y + x

{x - y = 3,

{x - y = 3,{(10x + y) - (10y + x) = 27;

Let's make x the subject from the 1st equation (it doesn't matter which equation or term (x or y) you choose):

x = 3 + y

Replace x in the 2nd equation with its new value from the 1st one:

(10 × (3 + y) + y ) - (10y + (3 + y)) = 27

30 + 10y + y - 10y - 3 - y = 27

Collect like-terms (also, when moving the terms to the other side, make sure to change their sign into the opposite of the previous one):

0y = 0

y = 0

x = 3 + 0 = 3