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 = 1.2 × (10x + y) + 11

Multiplying both sides by 5, 
50y + 5x = 60x + 6y + 55 
⇒ 55x − 44y = −55  …. (I)

And, x + y = 8  …. (II)

From (II), x = 8 − y. Substitute in (I): 
55(8 − y) − 44y = −55 
440 − 99y = −55 
99y = 495 
y = 5

Then x = 8 − 5 = 3. 
So, original number = (10 × 3 + 5) = 35.