Subject: General Aptitude · Chapter: Time and Work · Exam: 2005 · Marks: · Difficulty:
A man and a boy together can do a certain amount of digging in 40 days. Their speeds in digging are in the ratio of 8 : 5. How many days will the boy take to complete the work if engaged alone?
(a)52 days
(b)68 days
(c)80 days
(d)104 days
Answer
Answer (as printed):
Explanation
Ratio of digging speeds of man and boy $=8 : 5$. Ratio of times taken by man and boy $=5 : 8$. Suppose the man takes $5x$ days while the boy takes $8x$ days to complete the work alone. Then, $\frac{1}{5x}+\frac{1}{8x}=\frac{1}{40} \Rightarrow \frac{13}{40x}=\frac{1}{40} \Rightarrow x=13$. Hence, time taken by the boy to complete the work alone $=(8 \times 13)$ days $=104$ days.
Explanation as extracted from the printed page; notation may be imperfect.