Subject: General Aptitude · Chapter: Time and Work · Exam: 2010 · Marks: · Difficulty:
Madhu takes twice as much time as Uma to complete a work and Rahul does it in the same time as Madhu and Uma together. If all three working together can finish the work in 6 days, then the time taken by Madhu to finish the work is
(a)12 days
(b)14 days
(c)36 days
(d)40 days
Answer
Answer (as printed): C
Explanation
Suppose Uma takes $x$ days to complete the work. Then, Madhu takes $2x$ days. Uma's 1 day's work $=\frac{1}{x}$; Madhu's 1 day's work $=\frac{1}{2x}$. Rahul's 1 day's work = (Madhu+Uma)'s 1 day's work $=\frac{1}{2x}+\frac{1}{x}=\frac{3}{2x}$. (Rahul+Madhu+Uma)'s 1 day's work $=\frac{3}{2x}+\frac{1}{2x}+\frac{1}{x}=\frac{6}{2x}=\frac{3}{x}$. $\therefore \frac{3}{x}=\frac{1}{6} \Rightarrow x=18$. Hence, Madhu takes $(2 \times 18)=36$ days to complete the work.
Explanation as extracted from the printed page; notation may be imperfect.