Question
Sat February 23, 2013 By:

A two-digit number is 4 times the sum if its digits and twice the products of its digits. Find the number.

Expert Reply
Sat February 23, 2013
Let the ones digit of the number be x and the tens digit be y and hence the number would be 10y+x
 
Since, the 2 digit number is 4 times the sum of its digit, therefore
10y+x = 4(x+y)
6y = 3x
x = 2y
 
Also, the 2 digit number is twice the product of its digit, therefore
10y+x = 2xy
Substituting for x
10y + 2y = 4y
4y2  = 12y
y = 3y
Since, y can't be equal to 0, therefore y = 3 and hence, x = 6. 
So, the number is 36.
 
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