Question

A two digit no. is 4 times the sum of its digits and twice the product of the digits. find the no.
give step by step answer

Answer 1

Let the two digit number be xy having tens digit as x and unit digit as y which is simply written as 10x+y

Two digit number=10x+y and sum of its digits=x+y

Given, two digit number is four times the sum of its digits.

10x+y=4(x+y)

10x+y=4x+4y

10x-4x=4y-y

6x=3y

2x=y =>y=2x -------> (1)

Product of the digits=xy

Also, the two digit  number is twice the product of its digits

10x+y=2xy

substitute eqn (1) i.e., y=2x in the above eqn.

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

12x=4x*x

12=4x

x=12/4=3=>x=3

Substitute x=3 in eqn. (1)

y=2x=>y=2(3)=6=>y=6

Therefore, x=3 and y=6

Hence the two digit number is xy=36.