A) \[11{\scriptstyle{}^{1}/{}_{4}}\]days
B) \[5{\scriptstyle{}^{1}/{}_{4}}\] days
C) \[\text{9}{\scriptstyle{}^{1}/{}_{4}}\] days
D) \[\text{10}{\scriptstyle{}^{1}/{}_{4}}\] days
Correct Answer: D
Solution :
(d) In 1 day, A completes \[\frac{1}{9}\]work In 1 day, B completes \[\frac{1}{12}\] work. If they work on alternate day, completion of work (till it gets fully completed) will follow the pattern:- \[\frac{1}{9}+\frac{1}{12}+\frac{1}{9}+\frac{1}{12}+.....\] now, \[\frac{7}{36}*5=\frac{35}{36}\] \[\Rightarrow \]In 10 days, \[\frac{35}{36}\] work will be over. \[\Rightarrow \]work left \[=1-\frac{35}{36}=\frac{1}{36}\] This A will able to complete in \[\frac{\frac{1}{36}}{\frac{1}{9}}=\frac{1}{4}\] days \[\Rightarrow \left( 10+\frac{1}{4} \right)\]days =\[10+\frac{1}{4}\]days.
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