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Question

$$A$$ can do a piece of work in 25 days and $$B$$ in 20 days. They work together for 5 days and then $$A$$ goes away. In how many days will $$B$$ finish the remaining work?


A
17 days
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B
11 days
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C
10 days
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D
None of these
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Solution

The correct option is B 11 days
A's 1 day's work $$ = \dfrac{1}{25}$$
Similarly, B's 1 day's work $$ = \dfrac{1}{20}$$
A's and B's together 1 day's work
$$\dfrac { 1 }{ 25 } +\dfrac { 1 }{ 20 } =\dfrac { 4 }{ 100 } +\dfrac { 5 }{ 100 } =\dfrac { 4+5 }{ 100 } =\dfrac { 9 }{ 100 }$$
Their 5 day's work together = 5 x 1 day's work
$$1-\dfrac { 45 }{ 100 } =\dfrac { 100 }{ 100 } -\dfrac { 45 }{ 100 } =\dfrac { 100-45 }{ 100 } =\dfrac { 55 }{ 100 }$$
Now, this remaining work is done by B.
Let B takes $$x$$ days to complete it.
$$\dfrac { 1 }{ 20 } \times x=\dfrac { 55 }{ 100 } \\ \Rightarrow x=\dfrac { 55 }{ 100 } \times 20\\ \Rightarrow x=\dfrac { 55 }{ 5 } \\ \Rightarrow x=11$$
Hence, B will finish the remaining work in $$11$$ days.

Mathematics

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