| A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days? |
A) 11 days
B) 13 days
C) \[20\frac{3}{17}\,\,\text{days}\]
D) None of these
Correct Answer: B
Solution :
| Ratio of times taken by A and |
| \[B=100:130=10:13\] |
| Suppose B takes x days to do the work. |
| Then, \[10:13::23:x\] |
| \[\Rightarrow \] \[x=\left( \frac{23\times 13}{10} \right)\]\[\Rightarrow \]\[x=\frac{299}{10}\] |
| A's 1 days work \[=\frac{1}{23};\] B's 1 day's work \[=\frac{10}{299}.\] |
| \[(A+B)'s\]1 day's work\[=\left( \frac{1}{23}+\frac{10}{299} \right)=\frac{23}{299}=\frac{1}{13}\] So, A and B together can complete the job in 13 days. |
| Alternate Method |
| Let A takes x days to complete the work, then B will take \[x+\frac{30x}{100}=\frac{13x}{10}\,\text{days}\] |
| If they work together, \[(A+B)'s\] 1 day work |
| \[=\frac{1}{x}+\frac{10}{13x}=\frac{23}{13x}\] |
| Here, \[x=23\](as A can complete the work alone in 23 days) |
| \[\Rightarrow \] \[(A+B)'s\]1day work \[=\frac{23}{13\times 23}=\frac{1}{13}\] |
| \[\therefore \] Together they can complete the work in 13 days. |
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