Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?
(a)6 days
(b)10 days
(c)15 days
(d)20 days
Answer
Answer (as printed): B
Explanation
Work done by X in 4 days $=\left(\frac{1}{20} \times 4\right)=\frac{1}{5}$. Remaining work $=\left(1-\frac{1}{5}\right)=\frac{4}{5}$. (X+Y)'s 1 day's work $=\left(\frac{1}{20}+\frac{1}{12}\right)=\frac{2}{15}$. Now, $\frac{2}{15}$ work is done by X and Y in 1 day. So, $\frac{4}{5}$ work will be done by X and Y in $\left(\frac{4}{5} \times \frac{15}{2}\right)=6$ days. Hence, total time taken $=(6+4)$ days $=10$ days.
Explanation as extracted from the printed page; notation may be imperfect.