Question
Download Solution PDF4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 8 men and 6 women take to do the same job?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
4 men + 3 women finish a job in 6 days.
5 men + 7 women finish the same job in 4 days.
Formula Used:
M1 × D1 = M2 × D2 (when work is constant)
Let the work done by 1 man in 1 day be 'm' units.
Let the work done by 1 woman in 1 day be 'w' units.
Total work = (Number of men × work per man per day + Number of women × work per woman per day) × Number of days
Calculation:
From the first statement, total work = (4m + 3w) × 6
⇒ 24m + 18w = Total Work (Equation 1)
From the second statement, total work = (5m + 7w) × 4
⇒ 20m + 28w = Total Work (Equation 2)
Equating Equation 1 and Equation 2 (since the total work is the same):
24m + 18w = 20m + 28w
⇒ 24m - 20m = 28w - 18w
⇒ 4m = 10w
⇒ m = 10w / 4
⇒ m = 2.5w
Substitute the value of m in Equation 1 to find the total work in terms of 'w':
Total Work = 24(2.5w) + 18w
⇒ Total Work = 60w + 18w
⇒ Total Work = 78w units
Now, let the number of days taken by 8 men and 6 women be 'D' days.
Work done by 8 men and 6 women in D days = (8m + 6w) × D
Substitute m = 2.5w:
(8(2.5w) + 6w) × D = Total Work
(20w + 6w) × D = 78w
26w × D = 78w
26D = 78
⇒ D = 78 / 26
⇒ D = 3
∴ 8 men and 6 women will take 3 days to do the same job.
Last updated on Jul 8, 2025
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