12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required ?
12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required ?
Answer is : 70
Explanation:
12 men can complete the work in 36 days.
12 × 36 men can complete the work in 1day.
Again, 18 women can complete the work in 60 days.
18 × 60 women can complete the work in1 day.
12 × 36 men = 18 × 60 women
2 men = 5 women
Now, 8 men + 20 women
= (4 × 5 + 20) women = 40 women
18 women complete the work in 60 days.
40 womens’ 20 days’ work
\(=\frac{40\times20}{18\times60}= \frac{20}{27}\)
\(\therefore\) Remaining work = \(1 - \frac{20}{27}= \frac{7}{27}\)
\(\therefore 18 \times 60\) women do 1 work in 1 day.
\(\therefore\) 1 woman does \(=\frac{ 1}{80 \times 60}\) Work in 1 day
\(\therefore\) 1 woman does in 4 days
\(= \frac{4}{180\times60} = \frac{1}{18\times15} \) work
\(\therefore \frac{1}{18 \times 15}\) work is done in 4 days by 1 woman
\(\therefore \frac{7}{27}\) work is done in 4 days by = \(\frac{18\times15\times7}{27}\)
= 70 days
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