(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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Time and Work and Wages

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Time and Work

$P$ can do $\left(\frac{1}{4}\right)$ of the work in $10$ days. $Q$ can do $40\%$ of the work in $40$ days and $R$ can do $\left(\frac{1}{3}\right)$ of the work in $13$ days. Who will complete the work first?

Medium

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$A, B$ and $C$ do a job in $6$ days,$12$ days and $15$ days respectively. After $\frac{1}{8}$ of the work is completed,$C$ leaves the job. The rest of the work is done by $A$ and $B$ together. What is the time taken to finish the remaining work? (in days)

Easy

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Subhash can copy $50$ pages in $10$ $h$,Subhash and Prakash can copy $300$ pages in $40$ $h$. In how much time can Prakash copy $30$ pages? (in $h$)

Medium

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Anu can complete a work in $10$ days. Manu is $25\%$ more efficient than Anu,and Sonu is $60\%$ more efficient than Manu. Working together,how long would they take to finish the job? (in days)

Medium

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If $12$ men and $16$ boys can do a piece of work in $5 \, \text{days}$,and $13$ men and $24$ boys can do it in $4 \, \text{days}$,then the ratio of the daily work done by a man to that of a boy is:

Medium

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$P$ can do $\left(\frac{1}{4}\right)$ of the work in $10$ days. $Q$ can do $40\%$ of the work in $40$ days and $R$ can do $\left(\frac{1}{3}\right)$ of the work in $13$ days. Who will complete the work first?

$A, B$ and $C$ do a job in $6$ days,$12$ days and $15$ days respectively. After $\frac{1}{8}$ of the work is completed,$C$ leaves the job. The rest of the work is done by $A$ and $B$ together. What is the time taken to finish the remaining work? (in days)

Subhash can copy $50$ pages in $10$ $h$,Subhash and Prakash can copy $300$ pages in $40$ $h$. In how much time can Prakash copy $30$ pages? (in $h$)

Anu can complete a work in $10$ days. Manu is $25\%$ more efficient than Anu,and Sonu is $60\%$ more efficient than Manu. Working together,how long would they take to finish the job? (in days)

If $12$ men and $16$ boys can do a piece of work in $5 \, \text{days}$,and $13$ men and $24$ boys can do it in $4 \, \text{days}$,then the ratio of the daily work done by a man to that of a boy is:

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