Ruby takes 2 days more than what Alia takes to produce x chairs

OFFICIAL ANSWER

They have to work together for 6 days to produce 24x chairs
So,they have to work together for 1 day to produce 4x chair(unitary method)......(1)
Ruby takes 2 more days to produce x chairs than Alia does
So,if Alia produces x chair in y days,Ruby produces x chair in (y+2) days
In y days , Alia produces x chairs ,so in 1 day , Alia produces x/y chair
In y+2 days ,Ruby produces x chair,so in 1 day ,Ruby produces x/(y+2) chair
So ,together in 1 day they produce x/y+x/(x+y) chair ....(2)
combining (1) and (2),
x/y+x/(x+y)=4x
=>4xy^2+6xy-2x=0
=>2y^2+3y-1=0
solving the equation with quadratic formula
x=(−b±\sqrt{b2−4ac})/(2a) we get,
y=-3±\sqrt{18}/4
By taking only the positive values ,we get the value of y to be an irrational number.So,the number of days Ruby needs to prepare 2x chair is also a irrational figure,which is not in the options.

ANSWER: E) None of these

Both work together for 6 days to produce 24x chairs.
This means both can produce x chairs in 6/24 or 1/4 day.

Let Alina take a days, so Ruby will take a+2 days to make x chairs.

\(\frac{1}{a}+\frac{1}{a+2}=4\)

\(a+2+a=4*a(a+2).......2a+2=4a^2+8a......4a^2+6a-2=0.....2a^2+3a-1=0\)
a=0.28 approx

So a+2=2.28


So Ruby takes 2.28 days for x chairs and will take 2*2.28=4.56 days for 2x chairs.

Of course it would have been better if the question had more friendly numbers.

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