(D) Let the work done by $A, B,$ and $C$ in one day be $A, B,$ and $C$ respectively.Given:$A + B = \frac{1}{30}$$B + C = \frac{1}{20}$$A + C = \frac{1

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(D) Let the work done by $A, B,$ and $C$ in one day be $A, B,$ and $C$ respectively.Given:$A + B = \frac{1}{30}$$B + C = \frac{1}{20}$$A + C = \frac{1}{15}$Adding these equations: $2(A + B + C) = \frac{1}{30} + \frac{1}{20} + \frac{1}{15} = \frac{2 + 3 + 4}{60} = \frac{9}{60} = \frac{3}{20}$.Therefore,$(A + B + C) = \frac{3}{20} \times \frac{1}{2} = \frac{3}{40}$.The time taken by all three working together is the reciprocal of their combined one-day work: $\frac{40}{3} = 13 \frac{1}{3} \text{ days}$.

Competitive Quantitative Aptitude Time and Work and Wages Time and Work

Medium

$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

A
$10$
B
$12$
C
$12 \frac{2}{3}$
D
$13 \frac{1}{3}$

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Time and Work and Wages

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Time and Work

$A$ can do a piece of work in $12$ days and $B$ in $15$ days. They work together for $5$ days and then $B$ leaves. The number of days taken by $A$ to finish the remaining work is:

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Twenty women together can complete a work in $16$ days. $16$ men together can complete the same work in $15$ days. The ratio of the working capacity of a man to that of a woman is

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$20$ women together can complete a work in $16$ days. $16$ men together can complete the same work in $15$ days. The ratio of the working capacity of a man to that of a woman is

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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 $days$):

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$P$ and $Q$ working together can complete a certain work in $6 \, \text{days}$. $Q$ alone can do it in $8 \, \text{days}$. In how many $\text{days}$ could $P$ alone finish the same work?

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$A$ and $B$ can complete a piece of work in $30 \text{ days}$,$B$ and $C$ can complete the same work in $20 \text{ days}$,and $A$ and $C$ can complete it in $15 \text{ days}$. If all of them work together,the time taken to complete the work will be? (in $days$)

Similar Questions

$A$ can do a piece of work in $12$ days and $B$ in $15$ days. They work together for $5$ days and then $B$ leaves. The number of days taken by $A$ to finish the remaining work is:

Twenty women together can complete a work in $16$ days. $16$ men together can complete the same work in $15$ days. The ratio of the working capacity of a man to that of a woman is

$20$ women together can complete a work in $16$ days. $16$ men together can complete the same work in $15$ days. The ratio of the working capacity of a man to that of a woman is

$A$ 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 $days$):

$P$ and $Q$ working together can complete a certain work in $6 \, \text{days}$. $Q$ alone can do it in $8 \, \text{days}$. In how many $\text{days}$ could $P$ alone finish the same work?

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