(B) Let the time taken by $A$ and $B$ together to complete the job be $x \, \text{days}$.Then, $A$ alone takes $(x + 27) \, \text{days}$ and $B$ alone

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(B) Let the time taken by $A$ and $B$ together to complete the job be $x \, \text{days}$.Then, $A$ alone takes $(x + 27) \, \text{days}$ and $B$ alone takes $(x + 3) \, \text{days}$.The work done by $A$ and $B$ in one day is $\frac{1}{x + 27} + \frac{1}{x + 3} = \frac{1}{x}$.Solving for $x$: $\frac{(x + 3) + (x + 27)}{(x + 27)(x + 3)} = \frac{1}{x}$.$\frac{2x + 30}{x^2 + 30x + 81} = \frac{1}{x}$.$2x^2 + 30x = x^2 + 30x + 81$.$x^2 = 81$, which gives $x = 9$.Thus, working together, they take $9 \, \text{days}$.

Competitive Quantitative Aptitude Time and Work and Wages Time and Work

Easy

$A$ alone would take $27 \, \text{days}$ more to complete the job than if both $A$ and $B$ worked together. If $B$ worked alone, he would take $3 \, \text{days}$ more to complete the job than $A$ and $B$ working together. What time would they take if both $A$ and $B$ worked together? (in $\text{days}$)

A
$7$
B
$9$
C
$11$
D
None of these

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Quantitative Aptitude Questions

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Time and Work and Wages

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Time and Work

$A$ and $B$ can do a piece of work in $30$ days,while $B$ and $C$ can do the same work in $24$ days and $C$ and $A$ in $20$ days. They all work together for $10$ days when $B$ and $C$ leave. How many days more will $A$ take to finish the work?

Difficult

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$A$ and $B$ working separately can do a piece of work in $9$ and $12$ days,respectively. If they work for a day alternately with $A$ beginning,the work would be completed in (in days):

Medium

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$P$ and $Q$ can do a piece of work in $30$ and $40$ days respectively. They began the work together,but $P$ left after some days and $Q$ finished the remaining work in $12$ days. After how many days did $P$ leave?

Medium

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$A$ and $B$ can do a work in $8$ days,$B$ and $C$ can do the same work in $12$ days. $A, B$ and $C$ together can finish it in $6$ days. $A$ and $C$ together will do it in (in days):

Medium

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$A$ is $50\%$ as efficient as $B$. $C$ does half of the work done by $A$ and $B$ together in the same time. If $C$ alone does the work in $20 \text{ days}$,then $A, B$,and $C$ together can do the work in (in $\text{days}$):

Medium

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$A$ and $B$ can do a piece of work in $30$ days,while $B$ and $C$ can do the same work in $24$ days and $C$ and $A$ in $20$ days. They all work together for $10$ days when $B$ and $C$ leave. How many days more will $A$ take to finish the work?

$A$ and $B$ working separately can do a piece of work in $9$ and $12$ days,respectively. If they work for a day alternately with $A$ beginning,the work would be completed in (in days):

$P$ and $Q$ can do a piece of work in $30$ and $40$ days respectively. They began the work together,but $P$ left after some days and $Q$ finished the remaining work in $12$ days. After how many days did $P$ leave?

$A$ and $B$ can do a work in $8$ days,$B$ and $C$ can do the same work in $12$ days. $A, B$ and $C$ together can finish it in $6$ days. $A$ and $C$ together will do it in (in days):

$A$ is $50\%$ as efficient as $B$. $C$ does half of the work done by $A$ and $B$ together in the same time. If $C$ alone does the work in $20 \text{ days}$,then $A, B$,and $C$ together can do the work in (in $\text{days}$):

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