6 men and 8 women can complete a work in 10 days. 26 men and 48 women ...
Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
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6 men and 8 women can complete a work in 10 days. 26 men and 48 women ...
Given Information:
- 6 men and 8 women complete a work in 10 days
- 26 men and 48 women complete the same work in 2 days
Calculating the work rate per person:
- Let the work be represented as W
- The work rate for 6 men and 8 women is W/10
- The work rate for 26 men and 48 women is W/2
Calculating the work rate per man and woman:
- Let the work rate for a man be M and for a woman be W
- From the given information, we can set up the equations:
6M + 8W = W/10
26M + 48W = W/2
Solving the equations:
- Simplifying the first equation, we get 60M + 80W = W
- Simplifying the second equation, we get 52M + 96W = W
- By solving these equations, we find M = 1/60 and W = 1/80
Calculating the work rate for 15 men and 20 women:
- The work rate for 15 men and 20 women is 15M + 20W = 15/60 + 20/80 = 1/4
Calculating the number of days needed:
- Let the number of days needed be D
- The total work is 1, so the work rate for 15 men and 20 women over D days is 1/D
- Setting up the equation, we get 1/4 = 1/D
- Solving for D, we find D = 4 days
Therefore, the work can be completed by 15 men and 20 women in 4 days.