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If 12 men can complete a project in 18 days and 15 women can complete the same project in 24 days, how many days will 8 men and 10 women working together take to complete the project?
12.5 ┬аdays
13.5 ┬аdays
14.4 ┬аdays
15.2 ┬аdays
13.5 ┬аdays
Use the inverse proportionality relation between the number of workers and the days required to finish a fixed amount of work to calculate results instantly.
12 men complete the project in 18 days, equivalent to 216 man-days.
Days=M2тАЛM1тАЛ├ЧD1тАЛтАЛ
Use the inverse proportionality relation between the number of workers and the days required to finish a fixed amount of work to calculate results instantly.
Forgetting that work and the number of workers are inversely proportional, which leads to incorrect direct multiplication.
Identify Given Parameters
Note that 12 men complete the project in 18 days.
M1тАЛ=12,D1тАЛ=18
Apply Work Formula
Calculate the total work in man-days using the inverse proportion product.
Total┬аWork=12├Ч18=216
Calculate Required Days
Divide the total man-days by the target number of workers to find the final duration.
Days=16216тАЛ=13.5
B is correct because 16 workers take 13.5 days to complete the project.
Understanding inverse proportionality between workers and time forms the foundation for solving compound proportion and pipe-cistern problems.
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