| 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 |
| \[\Rightarrow \] \[\frac{1}{a}-\frac{2}{a}=\frac{1}{5}-\frac{1}{4}\] |
| \[\Rightarrow \] \[\frac{1-2}{a}=\frac{4-5}{20}\] |
| \[\Rightarrow \] \[-\frac{1}{a}=-\frac{1}{20}\] |
| \[\Rightarrow \] \[\frac{1}{a}=\frac{1}{20}\] |
| \[\Rightarrow \] \[a=20\,\,\text{days}\] |
You need to login to perform this action.
You will be redirected in
3 sec
