A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work… · ABC26GN3504
Subject: General Aptitude · Chapter: Time and Work · Exam: S.S.C. 2007
$A$ and $B$ can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in
(a)$14 \frac{1}{3}$ days
(b)$15 \frac{2}{3}$ days
(c)$16 \frac{1}{3}$ days
(d)$18 \frac{2}{3}$ days
Answer
Answer (as printed): A
Explanation
(A+B)'s 2 days' work $=\left(\frac{1}{12}+\frac{1}{18}\right)=\frac{5}{36}$. Work done in 7 pairs of days $=\left(\frac{5}{36} \times 7\right)=\frac{35}{36}$. Remaining work $=\left(1-\frac{35}{36}\right)=\frac{1}{36}$. On the 15th day, it is A's turn. Now, $\frac{1}{12}$ work is done by A in 1 day. $\therefore \frac{1}{36}$ work is done by A in $\left(12 \times \frac{1}{36}\right)=\frac{1}{3}$ day. $\therefore$ Total time taken $=14\frac{1}{3}$ days.
Explanation as extracted from the printed page; notation may be imperfect.