Two workers A and B are engaged to do a piece | vedclass

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(C) Let the time taken by both $A$ and $B$ working together be $t 	ext{ h}$.Then,the time taken by $A$ alone is $(t + 8) 	ext{ h}$ and the time take

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$6$

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(C) Let the time taken by both $A$ and $B$ working together be $t 	ext{ h}$.Then,the time taken by $A$ alone is $(t + 8) 	ext{ h}$ and the time taken by $B$ alone is $(t + 4.5) 	ext{ h}$.The work done by $A$ and $B$ in $1 	ext{ h}$ is $\frac{1}{t+8} + \frac{1}{t+4.5} = \frac{1}{t}$.Solving for $t$:$\frac{(t+4.5) + (t+8)}{(t+8)(t+4.5)} = \frac{1}{t}$$t(2t + 12.5) = (t+8)(t+4.5)$$2t^2 + 12.5t = t^2 + 4.5t + 8t + 36$$2t^2 + 12.5t = t^2 + 12.5t + 36$$t^2 = 36$$t = 6 	ext{ h}$ (since time cannot be negative).Thus,they take $6 	ext{ h}$ to complete the job working together.

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