A number consists of two digits. The sum of the digits is 10. On reversing the digits of the number, the number decreases by 36. Find the product of the two digits.
Let the unit’s digit and ten’s place digit of the number be x and y respectively.
∴ Number = 10x + y
Now, according to the question,
x + y = 10 ----(1)
And,
10x + y = 10y + x + 36
⇒ 9x – 9y = 36
⇒ x – y = 4 ----(2)
Solving the equations (1) and (2), we get,
x = 7 and y = 3
∴ Required product of the two digits = 7 × 3 = 21