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.
Let the two digit number = 10x + y
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