8 men can finish a piece of work in 25 days. 15 women can finish the same piece of work in 16 days. 4 men and 8 women started working together and worked for 10 days. After that 6 more men joined them. How many days will they now take to finish the remaining work
Correct Answer: |
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D) 5\( \Large \frac{3}{5} \) |
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Description for Correct answer:
1 day work of 8 men = \( \Large \frac{1}{25} \)
1 day work of 1 man = \( \Large \frac{1}{25 x 8} \) = \( \Large \frac{1}{200} \)
1 day work of 15 women = \( \Large \frac{1}{16} \)
1 day work of 1 women = \( \Large \frac{1}{15 x 16} \) = \( \Large \frac{1}{240} \)
Work done by 4 men and 8 women in 10 days
= \( \Large \frac{4 x 10}{ 200} \) + \( \Large \frac{8 x 10}{240} \)
= \( \Large \frac{1}{5} \) + \( \Large \frac{1}{3} \) = \( \Large \frac{8}{15} \)
Remaining work = 1 - \( \Large \frac{8}{15} \) = \( \Large \frac{7}{15} \)
After 6 more men joined.
Work done by 10 men and 8 women in 1 day.
= \( \Large \frac{10}{200} \) + \( \Large \frac{8}{240} \) = \( \Large \frac{1}{20} \) + \( \Large \frac{1}{30} \) = \( \Large \frac{1}{12} \)
\( \Large \frac{1}{12} \)th of work completed in = 1 day
\( \Large \frac{7}{15} \)th of work completed in = \( \Large \frac{7}{15} \) x 12 = \( \Large \frac{28}{5} \)
5 \( \Large \frac{3}{5} \) days
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