Question

A two digits number is four times the sum of its digits and is also equal to twice the product of its digits. find the number

Answer 1

Let two digits be a & b,
then , 10a + b = the number
A two digit number is 4 times the sum of its digits
10a + b= 4(a+b)
10a + b = 4a + 4b
10a - 4a = 4b - b
6a = 3b
divide both sides by 3
2a = b

And twice the product of its digit.
10a + b = 2ab
put b = 2a
10a + 2a = 2×a×2a
12a = 4a×a
12 = 4a
Therefore, a = 3
then b = 2(3)
b = 6
Hence,the number = 36