| A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in |
A) \[13\frac{1}{3}\] days
B) 15 days
C) 20 days
D) 30 days
Correct Answer: A
Solution :
| (A's 1 day's work): (B's 1 day's work) |
| = 150: 100 = 3: 2 |
| Let A's and B's 1 day's work be 3x and 2x, respectively. |
| Then, C's 1 day's works \[=\left( \frac{3x+2x}{2} \right)=\frac{5x}{2}\] |
| \[\therefore \] \[\frac{5x}{2}=\frac{1}{40}\] |
| \[\Rightarrow \] \[x=\left( \frac{1}{40}\times \frac{2}{5} \right)=\frac{1}{100}\] |
| A's 1 day's work \[=\frac{3}{100},\] B's 1 day's work \[=\frac{1}{50},\] |
| C's 1 day's work \[=\frac{1}{40}\] |
| \[(A+B+C)'s\]1 day's work |
| \[=\left( \frac{3}{100}+\frac{1}{50}+\frac{1}{40} \right)=\frac{15}{200}=\frac{3}{40}\] |
| So, A, B and C are together can do the work in \[\frac{40}{3}\] |
| \[=13\frac{1}{3}\,\,days\] |
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