Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
A and B can complete a work in 18 days and 15 days respectively. They started doing the work together but after 3 days $A$ had to leave and $B$ alone completed the remaining work. The whole work was completed in
(a)$9 \frac{3}{4}$ days
(b)$10 \frac{1}{4}$ days
(c)$12 \frac{1}{2}$ days
(d)$12 \frac{3}{4}$ days
Answer
Answer (as printed): C
Explanation
(A+B)'s 1 day's work $=\left(\frac{1}{18}+\frac{1}{15}\right)=\frac{11}{90}$. (A+B)'s 3 days' work $=\left(\frac{11}{90} \times 3\right)=\frac{11}{30}$. Remaining work $=\left(1-\frac{11}{30}\right)=\frac{19}{30}$. Now, $\frac{1}{15}$ work is done by B in 1 day. $\therefore \frac{19}{30}$ work will be done by B in $\left(15 \times \frac{19}{30}\right)=\frac{19}{2}=9\frac{1}{2}$ days. Hence, total time taken $=\left(3+9\frac{1}{2}\right)$ days $=12\frac{1}{2}$ days.
Explanation as extracted from the printed page; notation may be imperfect.