Question

A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Answer 1

Let the digit in the ones place be x and tens place be y
Hence the two digit number = 10y + x
Given that the two digit number = 4 times sum of its digits
⇒ 10y + x = 4(x + y)
⇒ 10y + x = 4x + 4y
⇒ 3x – 6y = 0
⇒ 3x = 6y
∴ x = 2y → (1)
It is also given that the two digit number = 2 times product of its digits
⇒ 10y + x = 2xy
Divide by xy both the sides, we get

10/x + 1/y =2

put x =2y from 1, we get

6/y = 3

so y = 2 and hence x= 6
Hence x = 6
The two digit number is (10y + x) = 10(3) + 6 = 36