| A and B together can do a work in 12 days. B and C together do it in 15 days. If As efficiency is twice that of C, then the number of days required for B alone to finish the work, is |
A) 60
B) 20
C) 30
D) 15
Correct Answer: B
Solution :
| Let A can do the work in x days, then C can do the work in 2x days. Let B can do that work in y days. |
| \[\therefore \] \[\frac{1}{x}+\frac{1}{y}=\frac{1}{12}\] |
| \[\Rightarrow \] \[\frac{1}{y}=\frac{1}{12}-\frac{1}{x}\] |
| and \[\frac{1}{2x}+\frac{1}{y}=\frac{1}{15}\] |
| \[\Rightarrow \] \[\frac{1}{y}=\frac{1}{15}-\frac{1}{2x}\] |
| Solving, \[\frac{1}{12}-\frac{1}{x}=\frac{1}{15}-\frac{1}{2x}\] |
| \[\Rightarrow \] \[\frac{1}{x}-\frac{1}{2x}=\frac{1}{12}-\frac{1}{15}\] |
| \[\Rightarrow \] \[\frac{1}{2x}=\frac{5-4}{60}\]\[\Rightarrow \]\[x=30\] |
| \[\Rightarrow \] \[\frac{1}{y}=\frac{1}{12}-\frac{1}{x}=\frac{1}{12}-\frac{1}{30}\] |
| \[=\frac{5-2}{60}=\frac{3}{60}=\frac{1}{20}\] |
| \[\therefore \] \[y=20\] |
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