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(D) Let $A$ and $B$ together complete the work in $x$ days.Then,the time taken by $A = (x + 4)$ days.And,the time taken by $B = (x + 16)$ days.Accordi

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$8$

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(D) Let $A$ and $B$ together complete the work in $x$ days.Then,the time taken by $A = (x + 4)$ days.And,the time taken by $B = (x + 16)$ days.According to the work-rate formula,the sum of their individual work rates equals their combined work rate:$\frac{1}{x+4} + \frac{1}{x+16} = \frac{1}{x}$$\frac{(x+16) + (x+4)}{(x+4)(x+16)} = \frac{1}{x}$$\frac{2x + 20}{x^2 + 20x + 64} = \frac{1}{x}$$x(2x + 20) = x^2 + 20x + 64$$2x^2 + 20x = x^2 + 20x + 64$$x^2 = 64$$x = 8$ days.Therefore,they would take $8$ days to complete the work together.

If $A$ works alone,he would take $4$ days more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone,he would take $16$ days more to complete the job than if $A$ and $B$ work together. How many days would they take to complete the work if both of them worked together?

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