PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoIn the previous topics, we have learnt how to find the solution of the compound variation using the proportion method or multiplicative factor method or formula method.
Now, let us learn about the new concept called person days.
What do you mean by person days?
Person days is the number of persons working per day times the number of days.
Person days = Number of person \times Number of days
Also, remember that if x women or y men takes p days to complete the work, then a women and b men can complete the same work in \frac{xyp}{xb+ya} or \frac{p}{\frac{a}{x}+\frac{b}{y}} days.
Example:
1. In a construction site, if 20 women can complete a work in 7 days, how long will it take to complete the same work if 6 women left the work?
Solution:
Given that 20 women can complete a work in 7 days.
Person days = Number of persons \times Number of days
Person days = 20 \times 7 = 140
If 6 women left the work, then the number of persons become 20 - 6 = 14.
Now, substituting the number of persons and person days in the formula, we have:
140 = 14 \times days
\frac{140}{14} = days
10 = days
Therefore, it takes 10 days to complete the same work.
2. In a company, if 7 women or 3 men can complete a work in 90 days, then how long will it take for 8 women and 6 men to complete the same work?
Solution:
Person days method:
Let M denotes men and W denotes women.
Given that 7 women or 3 men can complete a work in 90 days.
Person days = Number of persons \times Number of days
Person days = 3M \times 90
Here, 7W = 3M
W = \frac{3}{7}M
Now, we have:
Number of persons = 8W + 6M = 8(\frac{3}{7}M) + 6M
= \frac{24}{7}M + 6M
= \frac{66}{7}M
Substituting the known values in the above formula, we have:
3M \times 90 = \frac{66}{7}M \times days
\frac{3M \times 90}{\frac{66}{7}M} = days
3M \times 90 \times \frac{7}{66M} = days
28.64 = days
Rounding off, we have 29 days.
Therefore, it takes 29 days to complete a work by 8 women and 6 men.
We can also determine the days using the formula method.
Formula method:
Let us determine the days using the formula \frac{xyp}{xb+ya}.
Here, x = 7, y = 3, p = 90, a = 8, b = 6
Number of days = \frac{xyp}{xb+ya}
= \frac{7 \times 3 \times 90}{(7 \times 6)+(3 \times 8)}
= \frac{1890}{42 + 24}
= \frac{1890}{66} = 28.64
Rounding off, we have 29 days.
(or)
Let us determine the days using the formula \frac{p}{\frac{a}{x}+\frac{b}{y}}.
Here, x = 7, y = 3, p = 90, a = 8, b = 6
Number of days = \frac{p}{\frac{a}{x}+\frac{b}{y}}
= \frac{90}{\frac{8}{7}+\frac{6}{3}}
= \frac{90}{\frac{24 + 42}{21}}
= \frac{90}{\frac{66}{21}}
= 90 \times \frac{21}{66}
= \frac{1890}{66} = 28.64
Rounding off, we have 29 days.
Therefore, it takes 29 days to complete a work by 8 women and 6 men.
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