Question

A two digit number is four times the sum of the digits . It is also equal to 3 times the product of digits . Find the number

Answer 1

A two digit positive integer can be expressed as 10x+y, where x is the tens digit and y is the ones digit. For example, 37 = 3(10)+7.

So, 10x+y = 4(x+y) and 10x+y = 3xy

10x+y = 4x+4y

6x = 3y

y = 2x

Since y = 2x and 10x+y = 3xy, we have 10x+2x=3x(2x)

12x = 6x2 6x2-12x = 0

6x(x-2) = 0 x = 0 or x = 2

Since x can't be zero, x = 2

y = 2x = 4

The number is 24.