Subject: General Aptitude · Chapter: Time and Work · Exam: 2005 · Marks: · Difficulty:
A man and a boy can do a piece of work in 24 days. If the man works alone for the last 6 days, it is completed in 26 days. How long would the boy take to do it alone?
(a)20 days
(b)24 days
(c)36 days
(d)72 days
Answer
Answer (as printed): D
Explanation
(M+B)'s 1 day's work $=\frac{1}{24}$. (M+B)'s 20 days' work + M's 6 days' work $=1 \Rightarrow$ M's 6 days' work $=\left(1-\frac{1}{24} \times 20\right)=\left(1-\frac{5}{6}\right)=\frac{1}{6} \Rightarrow$ M's 1 day's work $=\left(\frac{1}{6} \times \frac{1}{6}\right)=\frac{1}{36}$. $\therefore$ B's 1 day's work $=\left(\frac{1}{24}-\frac{1}{36}\right)=\frac{1}{72}$. Hence, the boy alone can do the work in 72 days.
Explanation as extracted from the printed page; notation may be imperfect.