Question : Two workers A and B are engaged to do a piece of work. Working alone A would take 8 hours more to complete the work than when working together. If B worked alone, would take $4\frac{1}{2}$ hours more than when working together. The time required to finish the work together is:
Option 1: 5 hours
Option 2: 4 hours
Option 3: 8 hours
Option 4: 6 hours
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Correct Answer: 6 hours
Solution :
Let A and B together take $x$ hours to complete the work.
Then, A alone takes $(x+8)$ hours to complete the work.
B alone takes $(x+\frac{9}{2})$ hours,
According to the question,
$\frac{1}{x+8}+\frac{1}{x+\frac{9}{2}}=1$
⇒ $\frac{1}{x+8}+\frac{2}{2x+9}=1$
⇒ $x(4x+25)=(x+8)(2x+9)$
⇒ $2x^2 =72$
⇒ $x^2 =36$
⇒ $x=6$
Hence, the correct answer is 6 hours.
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