(B) Let the work done by $(P+Q)$,$(Q+R)$,and $(R+P)$ in one day be $\frac{1}{30}$,$\frac{1}{40}$,and $\frac{1}{60}$ respectively.Adding these,we get $

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(B) Let the work done by $(P+Q)$,$(Q+R)$,and $(R+P)$ in one day be $\frac{1}{30}$,$\frac{1}{40}$,and $\frac{1}{60}$ respectively.Adding these,we get $2(P+Q+R) = \frac{1}{30} + \frac{1}{40} + \frac{1}{60}$.$2(P+Q+R) = \frac{4+3+2}{120} = \frac{9}{120} = \frac{3}{40}$.Therefore,$(P+Q+R)$ together can do the work in $2 \times \frac{40}{3} = \frac{80}{3} \, days$.

Competitive Quantitative Aptitude Time and Work and Wages Time and Work

Medium

$P$ 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
$\frac{40}{3}$
B
$\frac{80}{3}$
C
$\frac{160}{3}$
D
$\frac{20}{3}$

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Quantitative Aptitude Questions

Chapter

Time and Work and Wages

Subtopic

Time and Work

$A$ and $B$ can do a piece of work in $12$ days and $15$ days,respectively. They began to work together,but $A$ left after $4$ days. In how many more days would $B$ alone complete the remaining work?

Medium

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$A$ and $B$ complete a job in $12 \text{ days}$,while $A, B$,and $C$ can complete it in $8 \text{ days}$. $C$ alone will finish the job in (in $\text{days}$):

Medium

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If the wages of $45$ women amount to $Rs. 46575$ in $48$ days,how many men must work for $16$ days to receive $Rs. 17250$,given that the daily wage of a man is double that of a woman?

Medium

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If $A$ can complete a work in $16$ days,then in how many days can he complete $\frac{3}{4}$ of the work?

Medium

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Three men,four women and six children can complete a work in $7$ days. $A$ woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in $7$ days?

Difficult

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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 $days$)

Similar Questions

$A$ and $B$ can do a piece of work in $12$ days and $15$ days,respectively. They began to work together,but $A$ left after $4$ days. In how many more days would $B$ alone complete the remaining work?

$A$ and $B$ complete a job in $12 \text{ days}$,while $A, B$,and $C$ can complete it in $8 \text{ days}$. $C$ alone will finish the job in (in $\text{days}$):

If the wages of $45$ women amount to $Rs. 46575$ in $48$ days,how many men must work for $16$ days to receive $Rs. 17250$,given that the daily wage of a man is double that of a woman?

If $A$ can complete a work in $16$ days,then in how many days can he complete $\frac{3}{4}$ of the work?

Three men,four women and six children can complete a work in $7$ days. $A$ woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in $7$ days?

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