A two digit number is four times the sum and three times the product of its digit Find the number

A two digit number is four times the sum and three times the product o

1.	A two digit number is four times the sum and three times the product of its digit Find the number
Answer» Let the ten\'s digit of the required number be x and its unit\'s digit be y.As per given conditionA two-digit number is four times the sum of its digitsThen, 10x + y = 4(x + y){tex}\\Rightarrow{/tex} 6x - 3y = 0{tex}\\Rightarrow{/tex} 2x - y = 0......... (i)And A two-digit number is twice the product of its digits.Also, 10x + y = 2xy. ....... (ii)Putting y = 2x from (i) in (ii), we get10x\xa0+ 2x = 4x2{tex}\\Rightarrow{/tex} 4x2- 12 x = 0{tex} \\Rightarrow{/tex}\xa04x(x - 3) = 0{tex}\\Rightarrow{/tex} x -\xa03 = 0{tex}\\Rightarrow{/tex} x = 3 [ten\'s digit, x {tex}\\ne{/tex}\xa00]Putting x = 3 in (i), we get y = 6.Thus, ten\'s digit = 3 and unit\'s digit = 6.Hence, the required number is 36.