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 require digit be = (10x + y)

Then according to question

(10x + y) = 4(x + y)

(10x + y) = 4x + 4y

10x + y - 4x - 4y = 0

6x - 3y = 0

2x - y = 0

2x = y                          ................(1)

And, (10x + y) = 2xy                    .........(2)

Now putting the value of y in equation (2) from (1)

(10x + 2x) = (2x)(2x)

4x² - 12x = 0

4x(x - 3) = 0

x(x - 3) = 0

So, either

x = 0

Or

x - 3 = 0

x = 3

So, the digit can never be negative.

When x = 3 then 

y = 2x = 2 × 3 = 6

Therefore, number

=10x + y

= 10(3) + 6

= 30 + 6

= 36

Thus, the required number be 36.