A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.

x is the digit at the ten’s place and y is the digit at the unit’s place.

According to the conditions,

xy = 6 …(i) and

10x + y + 9 = x + 10y

→9x - 9y = -9

→ x - y = - 1 …(ii)

From (i) and (ii), we get

x = 2 and y = 3.

Therefore the two digit number = 10x + y = (10 × 2) + 3 = 23