  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  B
11 days  C
10 days  D
None of these  Solution

The correct option is B 11 daysA'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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