A man and a boy together can do a certain amount of digging in 40 days. Their speeds in digging are in the… · ABC26GN3432
Subject: General Aptitude · Chapter: Time and Work · Exam: R.R.B. 2005
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
No answer key was printed for this question.
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.