| A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone? |
A) 2: 5
B) 2: 7
C) 3: 7
D) 1: 6
E) 3: 5
Correct Answer: D
Solution :
| \[(A+B)'s\] 1 day's work \[=\frac{1}{20}\] |
| \[(B+C)'s\] 1 day's work \[=\frac{1}{30}\] |
| \[(C+A)'s\] 1 day's work \[=\frac{1}{40}\] |
| On adding, |
| \[2(A+B+C)'s\] 1 day's work \[=\frac{1}{20}+\frac{1}{30}+\frac{1}{40}\] |
| \[=\frac{6+4+3}{120}=\frac{13}{120}\] |
| \[\therefore \] \[(A+B+C)'s\]1 day's work \[=\frac{13}{240}\] |
| \[\therefore \] As 1 day's work |
| \[=\frac{13}{240}-\frac{1}{30}=\frac{13-8}{240}=\frac{5}{240}=\frac{1}{48}\] |
| C's 1 day's work \[=\frac{13}{240}-\frac{1}{20}=\frac{13-12}{240}=\frac{1}{240}\] |
| \[\therefore \] Required ratio \[=48:240=1:5\] |
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