| A work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days P alone can finish the work? |
A) 10
B) 20
C) 30
D) 60
Correct Answer: C
Solution :
| \[(P+Q)'s\]1 day's work \[=\frac{1}{12}\] ....(i) |
| \[(Q+R)'s\]1 day's work \[=\frac{1}{15}\] ....(ii) |
| \[(R+P)'s\]1 day's work \[=\frac{1}{20}\] ....(iii) |
| On adding Eqs. (i), (ii) and (iii), we get |
| \[2(P+Q+R)'s\]1 day's work |
| \[=\frac{1}{12}+\frac{1}{15}+\frac{1}{20}=\frac{5+4+3}{60}=\frac{12}{60}=\frac{1}{5}\] |
| \[\therefore \] \[(P+Q+R)'s\]1 day's work \[=\frac{1}{10}\] ....(iv) |
| \[\therefore \] P's 1 day s work \[=\,\,\frac{1}{10}-\frac{1}{15}=\frac{3-2}{30}=\frac{1}{30}\] |
| So, P alone will complete the work in 30 days. |
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