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Standard VII

Mathematics

Time and Work

A and B can...

Question

$A$ and $B$ can separately do a piece of work in $20$ and $15$ days respectively. They worked together for $6$ days after which $B$ was replaced by $C$ . If the work was finished in next $4$ days, then the number of days in which C alone could do the work will be

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Solution

(A + B)'s 6 day's work = $6 (\frac{1}{20} + \frac{1}{15}) = \frac{7}{10}$
(A + C)'s 4 day's work = $\frac{3}{10};$
(A + C)'s 1 day's work = $\frac{3}{40}$
A's 1 day's work = $\frac{1}{20}$
$∴$ C's day's work = $(\frac{3}{40} - \frac{1}{20}) = \frac{1}{40}$
Hence C alone can finish the work in 40 days

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A, B and C can separately do a work in 12, 15 and 20 days respectively. They started to work together but C left after 2 days. The remaining work will be finished in how many days?

Q. A can do a piece of work in 10 days , and B can do the same work in 20 days . With the help of C , they finished the work in 4 days . C can do the work in how many days, working alone ?

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can do a piece of work in

120

days and

B

can do it in

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days. They work together for

20

days. then,

B

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A

alone continues the work.

12

days after that

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C

do it. if he works alone?

A

and

B

together can do a piece of work in

12

days which

B

and

C

together can do in

16

days. After

A

has been working at it for

5

days and

B

for

7

days,

C

finishes it in

13

days. In how many days

C

alone will do the work ?

A

and

B

together can build a wall in

10

days;

B

and

C

working together can do it in

15

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A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be

(A + B)'s 6 day's work = 6(120+115)=710(A + C)'s 4 day's work = 310;(A + C)'s 1 day's work = 340A's 1 day's work = 120∴ C's day's work = (340−120)=140Hence C alone can finish the work in 40 days

$A$ and $B$ can separately do a piece of work in $20$ and $15$ days respectively. They worked together for $6$ days after which $B$ was replaced by $C$ . If the work was finished in next $4$ days, then the number of days in which C alone could do the work will be