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Question
A two-digit number is 4 times the sum of its digits and twice the product of digits. Find the number.
Solution
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`
⇒`3x=6y`
⇒`x=2y` ............(1)
Also
`10y+x=2xy`
⇒`10y+2y=2.2yy` [from(1)]
⇒`12y=4y^2`
⇒`y=3`
From (1), We get :
`x=2xx3=6`
∴ Original number=`10xx3+6=36`
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