A) \[17\frac{32}{35}\] days
B) \[19\frac{2}{3}\] days
C) \[16\frac{31}{37}\] days
D) \[18\frac{1}{3}\] days
Correct Answer: A
Solution :
\[(A+B)'s\] 1 day?s work \[=\frac{1}{30}+\frac{1}{20}=\frac{8}{150}\] \[\therefore \] \[(A+C)'s\] 1 days? work \[=\frac{1}{30}+\frac{1}{40}=\frac{7}{120}\] \[\therefore \] Work done in first 2 days \[=\frac{8}{150}+\frac{7}{120}=\frac{67}{600}\] Work done is \[8\times 2=16\] days \[=\frac{67\times 8}{600}=\frac{67}{75}\] Work left \[=1-\frac{67}{75}=\frac{8}{75}\] On 17th day \[(A+B)\] will work and they will finish \[\frac{8}{150}\] work. \[\therefore \] Work left \[=\frac{8}{75}-\frac{8}{150}=\frac{8}{150}=\frac{4}{75}\] On 18th day (A + C) will work and they will finish it in \[\frac{120}{7}\times \frac{4}{75}=\frac{32}{35}\] So, whole work will be done in \[17\frac{32}{35}\] days.
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