(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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(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.

Competitive Quantitative Aptitude Time and Work and Wages Time and Work

Medium

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?

A
$10$
B
$12$
C
$6$
D
$8$

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Time and Work and Wages

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Time and Work

$A, B$ and $C$ can do a piece of work in $16, 32$ and $48$ days,respectively. They started working together,but $C$ left after working $4$ days and $B$ left $2$ days before the completion of the work. The total number of days taken for the completion of the work was (in days):

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$A$ and $B$ can complete a piece of work in $45$ and $40$ days,respectively. They began the work together,but $A$ leaves after some days and $B$ completed the remaining work in $23$ days. After how many days did $A$ leave?

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$A$ man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy, can finish the work in $7$ days, in how many days will a boy do it alone?

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$A$ can finish a work in $24$ days,$B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are forced to leave after $3$ days. The remaining work was done by $A$ in (in days):

Medium

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While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (in days)

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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?

Similar Questions

$A, B$ and $C$ can do a piece of work in $16, 32$ and $48$ days,respectively. They started working together,but $C$ left after working $4$ days and $B$ left $2$ days before the completion of the work. The total number of days taken for the completion of the work was (in days):

$A$ and $B$ can complete a piece of work in $45$ and $40$ days,respectively. They began the work together,but $A$ leaves after some days and $B$ completed the remaining work in $23$ days. After how many days did $A$ leave?

$A$ man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy, can finish the work in $7$ days, in how many days will a boy do it alone?

$A$ can finish a work in $24$ days,$B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are forced to leave after $3$ days. The remaining work was done by $A$ in (in days):

While working $7$ hours a day,$A$ alone can complete a piece of work in $6$ days and $B$ alone in $8$ days. In what time would they complete it together,working $8$ hours a day? (in days)

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