Subject: General Aptitude · Chapter: Time and Work · Exam: 2005 · Marks: · Difficulty:
A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them, working alone, finish the whole work?
(a)2.5 days, 7.5 days
(b)5 days, 8.5 days
(c)5 days, 15 days
(d)None of these
Answer
Answer (as printed): C
Explanation
Suppose A takes $x$ days to finish the work alone and B takes $y$ days to finish the work alone. Then, $\frac{2}{x}+\frac{9}{y}=1$ ...(i). And, $\frac{3}{x}+\frac{6}{y}=1 \Leftrightarrow \frac{1}{x}+\frac{2}{y}=\frac{1}{3} \Leftrightarrow \frac{2}{x}+\frac{4}{y}=\frac{2}{3}$ ...(ii). Subtracting (ii) from (i), we get: $\frac{5}{y}=\frac{1}{3}$ or $y=15$. Putting $y=15$ in (i), we get: $\frac{2}{x}=\frac{2}{5}$ or $x=5$. Hence, A alone takes 5 days while B alone takes 15 days to finish the work.
Explanation as extracted from the printed page; notation may be imperfect.