| A and B together can do a work in 12 day, B and C together do it in 15 days. If A's efficiency is twice that of C, then the day- required for C alone to finish the work is |
A) 45 days
B) 50 days
C) 60 days
D) 70 days
Correct Answer: C
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. |
| \[\therefore \] \[\frac{1}{x}+\frac{1}{y}=\frac{1}{12}\] |
| \[\Rightarrow \] \[\frac{1}{y}=\frac{1}{12}-\frac{1}{x}\] (i) |
| and \[\frac{1}{2x}+\frac{1}{y}=\frac{1}{15}\] |
| \[\Rightarrow \] \[\frac{1}{y}=\frac{1}{15}-\frac{1}{2x}\] (ii) |
| From Eqs. (i) and (ii), we get |
| \[\frac{1}{12}-\frac{1}{x}=\frac{1}{15}-\frac{1}{2x}\] |
| \[\Rightarrow \] \[\frac{1}{2x}-\frac{1}{x}=\frac{1}{15}-\frac{1}{12}\] |
| \[\Rightarrow \] \[\frac{1-2}{2x}=\frac{4-5}{60}\] |
| \[\Rightarrow \] \[\frac{-1}{2x}=\frac{-1}{60}\]\[\Rightarrow \]\[x=30\] |
| \[\therefore \] C takes time \[=2\times 30=60\,days\] |
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