A man X can complete \(\frac{1}{3}\) of a job in 5 days and another man Y can…
2023
A man X can complete \(\frac{1}{3}\) of a job in 5 days and another man Y can complete \(\frac{2}{5}\) of the job in 10 days. In how many days can both X and Y together complete the job?
Answer: A. \(9\frac{3}{8}\) — ConceptA worker’s daily work rate equals the fraction of the job completed divided by the time taken. For people working together, add their daily rates; the…
- A.
\(9\frac{3}{8}\)
- B.
\(8\frac{3}{8}\)
- C.
\(9\frac{3}{5}\)
- D.
\(7\frac{7}{9}\)
Show answer & explanation
Correct answer: A
Concept
A worker’s daily work rate equals the fraction of the job completed divided by the time taken.
For people working together, add their daily rates; the completion time is the reciprocal of the combined rate.
Application
X’s rate is \(\frac{1}{3}\) ÷ 5 = \(\frac{1}{15}\) of the job per day.
Y’s rate is \(\frac{2}{5}\) ÷ 10 = \(\frac{1}{25}\) of the job per day.
Their combined rate is \(\frac{1}{15}+\frac{1}{25}=\frac{5+3}{75}=\frac{8}{75}\) of the job per day.
Thus, the required time is \(1÷\frac{8}{75}=\frac{75}{8}=9\frac{3}{8}\) days.
Cross-check
In \(\frac{75}{8}\) days, X completes \(\frac{5}{8}\) of the job and Y completes \(\frac{3}{8}\); together these fractions make one whole job.
Result
Therefore, both X and Y together complete the job in \(9\frac{3}{8}\) days.