30 persons can do a piece of work in 24 days. How many more persons are required to complete the work in 20 days?
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Work and Time: Calculating Additional Persons
This problem requires calculating the number of additional persons needed to complete a specific piece of work within a reduced timeframe. The core concept is inverse proportion: as the number of days decreases, the number of persons required increases proportionally.
Calculating Total Workload
First, establish the total effort needed for the work. This is typically measured in 'person-days', calculated by multiplying the initial number of persons by the number of days they take.
- Initial number of persons = 30
- Initial number of days = 24
- Total Work = Persons $\times$ Days
- Total Work = $30 \times 24$ person-days
- Total Work = $720$ person-days
Determining Persons for the New Deadline
Next, determine the total number of persons necessary to complete the same amount of work (720 person-days) within the new, shorter deadline of 20 days.
- Total Work = $720$ person-days
- Target days = 20
- Required Persons = Total Work / Target Days
- Required Persons = $ \frac{720}{20} $
- Required Persons = $36$
Finding the Number of Additional Persons
Finally, calculate how many more persons are needed by finding the difference between the number of persons required for the 20-day deadline and the original number of persons.
- Persons required for 20 days = 36
- Original number of persons = 30
- More Persons Required = Required Persons - Original Persons
- More Persons Required = $36 - 30$
- More Persons Required = $6$
Therefore, 6 more persons are needed to finish the work in 20 days.
Important Questions from Work Efficiency
A and B working together can complete a job in 30 days. The ratio of their efficiencies is 3 : 2. In how many days can the faster person complete the job?
A takes 15 days to complete \(\frac{5}{7} \) of a work. With the help of B, they finish the whole work in 12 days. In how many days, B alone will complete the same work
A alone can complete a work in 14 days and B alone can complete the same work in 21 days. A and B start the work together but A leaves the work after 4 days of the starting of work. In how many days B will complete the remaining work?
For completing a certain work, A is 50% less efficient than B and B is 50% more efficient than C. Working together A, B and C can complete the work in 48 days. A alone can complete the same work in:
X is twice as good as workman as Y. Together, they finish the work in 18 days. In how many days can it be done by each separately?
