Question
Download Solution PDFTwenty men or thirty women can complete a work in 40 days. In how many days will the 24 men and 24 women together complete the same work?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Twenty men or thirty women can complete a work in 40 days.
Formula Used:
Work = Number of people × Number of days
Combined work of men and women = Work / (Number of men + Number of women)
Calculation:
Let the total work be W.
Work done by 20 men in 40 days = W
Work done by 1 man in 1 day = W / (20 × 40)
Work done by 30 women in 40 days = W
Work done by 1 woman in 1 day = W / (30 × 40)
Work done by 24 men and 24 women together in 1 day:
Work done by 24 men in 1 day = 24 × (W / (20 × 40))
Work done by 24 women in 1 day = 24 × (W / (30 × 40))
Total work done by 24 men and 24 women in 1 day:
⇒ Work done in 1 day = 24 × (W / (20 × 40)) + 24 × (W / (30 × 40))
⇒ Work done in 1 day = (24W / 800) + (24W / 1200)
⇒ Work done in 1 day = (3W / 100) + (2W / 100)
⇒ Work done in 1 day = (5W / 100)
⇒ Work done in 1 day = W / 20
Therefore, the number of days required:
⇒ Number of days = Total work / Work done in 1 day
⇒ Number of days = W / (W / 20)
⇒ Number of days = 20
The number of days required for 24 men and 24 women to complete the work is 20 days.
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