(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

$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They began to do the work together,but $A$ leaves after some days and then $B$ completed the remaining work in $23$ days. The number of days after which $A$ left the work was:

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$10$ men and $15$ women together can complete a work in $6$ days. It takes $100$ days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

Medium

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$A$ tyre has two punctures. The first puncture alone would have made the tyre flat in $9 \,minutes$ and the second alone would have done it in $6 \,minutes.$ If air leaks out at a constant rate,how long does it take both the punctures together to make it flat? (in $minutes$)

Easy

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$P$ and $Q$ complete a certain work in $30 \, days$,$Q$ and $R$ in $40 \, days$,while $R$ and $P$ in $60 \, days$. How long will they take to finish it together? (in $days$)

Medium

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$A$ alone can do a piece of work in $6$ days and $B$ alone in $8$ days. $A$ and $B$ undertook to do it for $Rs. 3200$. With the help of $C$,they completed the work in $3$ days. How much is to be paid to $C$ (in $Rs.$)?

Difficult

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$A$ and $B$ can do a piece of work in $45$ days and $40$ days respectively. They began to do the work together,but $A$ leaves after some days and then $B$ completed the remaining work in $23$ days. The number of days after which $A$ left the work was:

$10$ men and $15$ women together can complete a work in $6$ days. It takes $100$ days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

$A$ tyre has two punctures. The first puncture alone would have made the tyre flat in $9 \,minutes$ and the second alone would have done it in $6 \,minutes.$ If air leaks out at a constant rate,how long does it take both the punctures together to make it flat? (in $minutes$)

$P$ and $Q$ complete a certain work in $30 \, days$,$Q$ and $R$ in $40 \, days$,while $R$ and $P$ in $60 \, days$. How long will they take to finish it together? (in $days$)

$A$ alone can do a piece of work in $6$ days and $B$ alone in $8$ days. $A$ and $B$ undertook to do it for $Rs. 3200$. With the help of $C$,they completed the work in $3$ days. How much is to be paid to $C$ (in $Rs.$)?

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