Question

a two digit number is four times the sum of its digit and twice the product of its digits .find the number

Answer 1

HELLO DEAR,

Let the digit in the ones place be x

------------------------- and -------------------------

tens place be y

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)

also, given that

the two digit number = 2 times product of its digits

=> 10y + x = 2xy

=> 10y + 2y =2×(2y)×y ---from(1)

=> 10y + 2y =4y²

=> 12y=4y²

=> y=12/4

=> y=3 ------put in--(1)

we get,

x=2×y

=> x=2×3

=> X=6 and Y =3

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