Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work ?
(a)$13 \frac{1}{3}$ days
(b)15 days
(c)20 days
(d)56 days
Answer
Answer (as printed): A
Explanation
Work done by X in 8 days $=\left(\frac{1}{40} \times 8\right)=\frac{1}{5}$. Remaining work $=\left(1-\frac{1}{5}\right)=\frac{4}{5}$. Now, $\frac{4}{5}$ work is done by Y in 16 days. Whole work will be done by Y in $\left(16 \times \frac{5}{4}\right)=20$ days. $\therefore$ X's 1 day's work $=\frac{1}{40}$, Y's 1 day's work $=\frac{1}{20}$. (X+Y)'s 1 day's work $=\left(\frac{1}{40}+\frac{1}{20}\right)=\frac{3}{40}$. Hence, X and Y will together complete the work in $\frac{40}{3}=13\frac{1}{3}$ days.
Explanation as extracted from the printed page; notation may be imperfect.