18 men can complete a project in 30 days and 16 women can complete the same project in 36 days. 15 men start working and after 9 days they are replaced by 18 women. In how many days will 18 women complete the remaining work?
Correct Answer: Description for Correct answer:
Let work done by 15 men in 9 days =\( \large w_{2}\)
\( \large\frac{M_{1}D_{1}}{W_{1}} = \frac{M_{2}D_{2}}{W_{2}} \)
\( \large\frac{18 \times 30}{1} = \frac{15 \times 9}{W_{2}}\)
= >\( \large W_{2} = \frac{15 \times 9}{18 \times 30} = \frac{1}{4} \)
Remaining work = \( \large 1 - \frac{1}{4} = \frac{3}{4}\)
16 women can complete the same project in 36 days, \( \large\frac{M_{1}D_{1}}{W_{1}} = \frac{M_{2}D_{2}}{W_{2}} \)
= >\( \large \frac{16 \times36}{1} = \frac{18 \times D_{2}}{\frac{3}{4}} \)
=>\( \large 18 \times D_{2} = \frac{3}{4}\times 16 \times 36 \)
\( \large D_{2} = 24 days \)
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