Question

A two digit number is four times the number of the digit and twice the product of the digit0.give reason in support of your answer.t

Answer 1

Let the digits be x and y.

Then the number is 10x + y.

Since the number is 4 times the sum of the digits, we get

10x + y = 4(x + y)

i.e. 10x + y = 4x + 4y

or 6x = 3y. This gives, y = 2x.

Also, the number is twice the product of the digits.

thus, 10x + y = 2xy

Substituting the value of y = 2x in the second equation, we get

10x + 2x = 2x * 2x

Thus, 12x = 4x^2

or 12 = 4x.

Therefore, x = 12 / 4 = 3.

Then, y = 2x = 2 * 3 = 6.

Therefore, the number is 10 * 3 + 6 = 36.

Check.

36 = 4 (3 + 6) = 4* 9

and 36 = 2 * (3*6) = 2*18

Thus, the number is 36.