5 men can complete a work in 16 days, which 8 women can complete in 36 days. If 10 men started the work and after 4 days, 12 women joined them then find the total time taken to complete the work.
This questions was previously asked in
RRB PO Prelims (05 Aug, 2023 Shift 2)
None of these
Incorrect AnswerExplanation:
- Total work by 5 men: 5 men complete work in 16 days. Thus, total work = 5 × 16 = 80 man-days.
- Work rate of 1 man: 80 man-days / 5 = 16 days.
- Total work by 8 women: 8 women complete work in 36 days. Thus, total work = 8 × 36 = 288 woman-days.
- Work rate of 1 woman: 288 woman-days / 8 = 36 days.
- Equivalent men to women work rate: 1 man's work rate for 1 day = 36/16 = 2.25 times a woman's daily rate.
- Initial work by 10 men for 4 days: Work done = 10 men × 4 days = 40 man-days. Remaining work = 80 - 40 = 40 man-days.
- Work when 12 women join: Convert 12 women to equivalent men = 12 / 2.25 = approximately 5.33 men.
- Effective workforce now: 10 men + 5.33 men (women equivalent) = 15.33 men.
- Remaining work completed by combined workforce: Time = 40 man-days / 15.33 men ˜ 2.61 days.
- Total time: 4 days + 2.61 days ˜ 6.61 days, which can be rounded to 7 days.
Correct Answer: ? Option 3 - 7
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By: Parvesh Mehta