Working together A and B can complete a piece of work in 5 days. If A had worked twice as fast the work would have been completed in 4 days. In how many days can A alone complete the work? |
A) \[20\,\,\text{days}\]
B) \[6\frac{2}{3}\,\,\text{days}\]
C) \[18\,\,\text{days}\]
D) \[6\frac{1}{4}\,\,\text{days}\]
Correct Answer: A
Solution :
Let A do the work in a days. |
\[\therefore \]A's 1 day's work \[=\frac{1}{a}\] |
Let B do the work in b days, |
\[\therefore \]B's 1 day's works \[=\frac{1}{b}\] |
According to the question, |
\[\frac{1}{a}+\frac{1}{b}+\frac{1}{5}\] (i) |
\[\frac{2}{a}+\frac{1}{b}=\frac{1}{4}\] (ii) |
On solving Eqs. (i) and (ii)i we get |
\[\Rightarrow \] \[\frac{1}{a}-\frac{2}{a}=\frac{1}{5}-\frac{1}{4}\] |
\[\Rightarrow \] \[\frac{1-2}{a}=\frac{4-5}{20}\] |
\[\Rightarrow \] \[-\frac{1}{a}=-\frac{1}{20}\] |
\[\Rightarrow \] \[\frac{1}{a}=\frac{1}{20}\] |
\[\Rightarrow \] \[a=20\,\,\text{days}\] |
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