When the digits of a two-digit number are interchanged,

Solution

Let the unit digit and tens digit of the original number be ‘y’ and ‘x’, respectively.
Original number = (10x + y)

According to the data given: 
10y + x = 1.5 × (10x + y) − 5

Multiplying both sides by 2, 
20y + 2x = 30x + 3y − 10 
⇒ 28x − 17y = 10  …. (I)

And, x + y = 10  …. (II)

From (II), x = 10 − y. Substitute in (I): 
28(10 − y) − 17y = 10 
280 − 45y = 10 
45y = 270 
y = 6

Then x = 10 − 6 = 4. 
So, original number = (10×4 + 6) = 46.