Question

A two-digit number is four times the sum of its digits and twice the product of its digits. Find the number.

Answer 1

Let the tens and the units digits of the required number be x and y​, respectively.
Required number = (10x + y)
∴ 10x + y = 4(x + y)
⇒ 10x + y = 4x + 4y
⇒ 6x − 3y = 0
⇒ 2x − y = 0 or y = 2x ....(i)
Again, we have:
10x + y = 2xy ....(ii)
On substituting y = 2x in (ii), we get:
10x + 2x = 2x(2x)
12x = 4x²
4x = 12
⇒ x = 3
On substituting x = 3 in (i), we get:
2 × 3 − y = 0
⇒ y = 6
∴ Number = (10x + y) = 10 × 3 + 6 = 30 + 6 = 36
Hence, the required number is 36.