Q. 244.1( 7 Votes )

A two – digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Answer :

Let the digits at units and tens places be x and y respectively.

Original number = 10y + x


According to the question


10y + x = 4(x + y)


10y + x = 4x + 4y


3x – 6y = 0


x = 2y – – – – (1)


also,


10y + x = 2xy


Using (1)


10y + 2y = 2.2y.y


12y = 4y2


y = 3


From (1) we get


x = 2.3 = 6


Original number = 10y + x


= (10.3) + 6 = 36


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