A) \[2\frac{1}{13}\]days
B) \[3\frac{2}{13}\]days
C) \[4\frac{2}{13}\]days
D) \[7\frac{2}{13}\]days
E) None of these
Correct Answer: E
Solution :
B works alone for 20 days \[\therefore \] Work done by B in 20 days\[=\frac{20}{30}=\frac{2}{3}\] \[\therefore \](A + B) do together\[\left( 1-\frac{2}{3} \right)=\frac{1}{3}\]work Now, (A + B) can do 1 work in\[\frac{30\times 35}{30+35}\]\[=\frac{1050}{65}=\frac{210}{13}\]days \[\therefore \](A + B) can do\[\frac{1}{3}\]work in\[\frac{210}{13}\times \frac{1}{3}\]days \[\text{=}\frac{\text{70}}{\text{13}}\text{days}\,\,\text{=}\,\,\text{5}\frac{\text{5}}{\text{13}}\text{days}\] Hence A left the work after\[\text{5}\frac{5}{13}\]days Method II: LCM of 35 and 30 =210 \[\therefore \]A's one day's work \[=\frac{210}{35}=6\] units/day B s one day's work \[=\frac{210}{30}=7\] units/day B's work in 20 days \[=20\times 7=140\] units \[\therefore \]Remaining work \[=(210-140)=70\] units 70 units of work is done by (A + B) in\[\frac{70}{6+7}\] \[=\frac{70}{13}\]days\[=5\frac{5}{13}\text{days}\] Hence A left the work in\[\left( \frac{70}{13}= \right)5\frac{5}{13}\text{days}\]
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