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Question
Divide 27 into two parts such that the sum of their reciprocal is `3/20`
Solution
Let the two parts be x and `(27-x)`
According to the given condition,
`1/x+1/(27-x)=3/20`
⇒`( 27-x+x)/(x(27-x))=3/20`
⇒`27/(27x-x^2)=3/20`
⇒`27x-x^2=180`
⇒`x^2-27x+180=0`
⇒`x^2-15x-12x+180=0`
⇒`x(x-15)-12(x-15)=0`
⇒`(x-12)(x-15)=0`
⇒`x-12=0 or x-15=0`
⇒`x=12 or x-15`
When x=12,
`27-x=27-12=15`
When` x=15`
`27-x=27-15=15`
Hence, the required parts are 12 and 15.
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