# A two digit number is 4 times the sum

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

Sol: let the digits be x and y
let x is in the tens place then
it sill become 10x let y is in once place the it will become
1y
the original number be 10x+y
from the question
10x+y=4(x+y)
10x+y=4x+4y
10x-4x+y-4y=0
6x-3y=0
2x-y=0
2x=y. eq-1
again according to question
10x+y=2(xy)
substitute y=2x
10x+2x=2x(2x)
12x/2x=2x
6=2x
x=3
if x=3 then y=?
2x=y
y=6
the number is 36

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