Question

If two digit number is four times the sum of its digits and twice the product of 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

(10/2y) + (1/y) = 2

(5/y) + (1/y) = 2

(6/y) = 2

y = 3 ;

Hence x = 6 ,

the two digit number is ( 10y + x ) = 10(3) + 6 = 36