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
Three workers, X, Y, and Z, can complete a certain job in 10 days, 12 days, and 15 days, respectively. Determine the number of days required for them to complete the job when they work together.
If 5 workers, working at the same rate, complete a job in 12 days, how many days will 10 workers take to complete the same job?
- A piece of work can be done by 16 men in 8 days working 12 hours a day. How many men are needed to complete another work, which is three times the first one, in 24 days working 8 hours a day?
- Ajay can do a painting in 12 days. Amit is 70% more efficient than Ajay. What is the number of days Amit would need to finish the same painting?
Important Questions from Time and work
In a circular race on a track of length 2000 m, X and Y start from the same point at the same time in opposite directions at the speeds of 15 km/h and 33 km/h, respectively. After how much time will they meet next?
Which of the following option figures will complete the pattern in the figure given below?
A has completed two-third of a job in 8 days, and B completes the rest of the job in 20 days. In how many days can they together complete the job?
The smallest 4-digit prime number is:
If Anand can do a piece of work in 9 days and Vinod can complete the same work in 6 days, then in how many days will both of them complete it together?
