Question

$A$ and $B$ together can complete a task in $7$ days. $B$ alone can do it in $20$ days. What part of the work was carried out by $A$?
$I$. $A$ completed the job alone after $A$ and $B$ worked together for $5$ days.
$II$. Part of the work done by $A$ could have been done by $B$ and $C$ together in $6$ days.

• A. $I$ alone sufficient while $II$ alone not sufficient to answer
• B. $II$ alone sufficient while $I$ alone not sufficient to answer
• C. Either $I$ or $II$ alone sufficient to answer
• D. Both $I$ and $II$ are not sufficient to answer
• E. Both $I$ and $II$ are necessary to answer

Answer 1

The correct option is A $I$ alone sufficient while $II$ alone not sufficient to answer

$B$'s $1$ day's work $=\frac{1}{20}$
$(A+B)$'s $1$ day's work $=\frac{1}{7}$
$I$. $(A+B)$'s $5$ day's work $=\frac{5}{7}$
Remaining work $=(1-\frac{5}{7})=\frac{2}{7}$
$\therefore$ $\frac{2}{7}$ work was carried by $A$.
$II$. is irrelevant.
$\therefore$ Correct answer is (A).