Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which $C$ alone could do the work will be
(a)30
(b)35
(c)40
(d)60
Answer
Answer (as printed): C
Explanation
(A+B)'s 6 days' work $=6\left(\frac{1}{20}+\frac{1}{15}\right)=\frac{7}{10}$. (A+C)'s 4 days' work $=\left(1-\frac{7}{10}\right)=\frac{3}{10}$. $\therefore$ (A+C)'s 1 day's work $=\frac{3}{40}$. A's 1 day's work $=\frac{1}{20}$. $\therefore$ C's 1 day's work $=\left(\frac{3}{40}-\frac{1}{20}\right)=\frac{1}{40}$. Hence, C alone can finish the work in 40 days.
Explanation as extracted from the printed page; notation may be imperfect.