Calculating Work Rates
First, let's determine the amount of work one man and one woman can do in a single day.
- Work done by 8 men in 20 days = 1 job.
- Work done by 1 man in 1 day = \(\frac{1}{8 \times 20} = \frac{1}{160}\) of the job.
- Work done by 8 women in 32 days = 1 job.
- Work done by 1 woman in 1 day = \(\frac{1}{8 \times 32} = \frac{1}{256}\) of the job.
Calculating Combined Daily Work
Next, find the total work done by 5 men and 8 women in one day.
- Work done by 5 men in 1 day = \(5 \times \frac{1}{160} = \frac{5}{160} = \frac{1}{32}\) of the job.
- Work done by 8 women in 1 day = \(8 \times \frac{1}{256} = \frac{8}{256} = \frac{1}{32}\) of the job.
- Combined work by 5 men and 8 women in 1 day = \(\frac{1}{32} + \frac{1}{32} = \frac{2}{32} = \frac{1}{16}\) of the job.
Calculating Total Time Required
Finally, calculate the total days needed to complete the job with the combined workforce.
- Time = \(\frac{\text{Total Work}}{\text{Combined Work Rate per day}}\)
- Time = \(\frac{1 \text{ job}}{\frac{1}{16} \text{ job/day}} = 1 \times \frac{16}{1} = 16\) days.
Therefore, 5 men and 8 women together will complete the job in 16 days.
Similar Questions
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Important Questions from Time and work
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