Five men started a job expected to be done in 15 days. After 5 days, 10 women joined them and together they finished in the next 5 days. If 10 women alone had started the job, in how many days would they have completed it?
Aptitude
Time and Work
Difficulty: Medium
Choose an option
Answer
Correct Answer: 15 days
Explanation
Introduction / Context:Infer women-to-man efficiency from the mixed phase, then apply it to compute the time for 10 women to complete the full job alone.
Given Data / Assumptions:
- 5 men for 15 days → job size = 75 man-days.
- After 5 days (25 man-days done), 10 women join and the remaining is done in 5 more days.
Concept / Approach:Use remaining work and team rate over the next 5 days to deduce 1 woman in man-equivalents, then compute the women-only time.
Step-by-Step Solution:
Remaining work after 5 days = 75 - 25 = 50 man-daysIn next 5 days: (5 men + 10 women)*5 days = 50 → 25 man-days + 50 woman-days = 50Thus, 50 woman-days = 25 man-days → 1 woman-day = 1/2 man-dayWomen-only rate (10 women) = 10 * (1/2) = 5 man-days/dayTime = 75 / 5 = 15 daysVerification / Alternative check:Back-substitution to mixed phase confirms consistency with the observed completion time.
Why Other Options Are Wrong:They reflect incorrect conversion between women and men or wrong total job size.
Common Pitfalls:Confusing “man-days” with “men-days” arithmetic; always treat efficiency conversion consistently.
Final Answer:15 days