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8 men can complete a work in 12 days, 4 women can complete it in 48 days and 10 children can complete the same work in 24 days. In how many days can 10 men, 4 women and 10 children complete the same work?
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A) 10 days |
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B) 5 days |
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C) 7 days |
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D) 6 days |
Correct Answer:
| D) 6 days |
Description for Correct answer:
1 man can finish the work in \( \Large 8 \times 12 \) = 96 days
1 woman can finish the work in \( \Large 4 \times 48 \) = 1 92 days
1 child can finish the work in \( \Large 10 \times 24 \) = 240 days
1 man's 1 day's work = \( \Large \frac{1}{96} \)
1 woman's 1 day's work = \( \Large \frac{1}{192} \)
1 child's 1 day's work = \( \Large \frac{1}{240} \)
(10 men + 4 women + 10 children)'s 1 day's work
= \( \Large \left(\frac{10}{96}+\frac{4}{192}+\frac{10}{240}\right) \)
= \( \Large \left(\frac{5}{48}+\frac{1}{48}+\frac{1}{24}\right) \)
=\( \Large \left(\frac{5+1+2}{48}\right) \)
= \( \Large \frac{8}{48} = \frac{1}{6} \)
Hence, they will finish the work in 6 days.
1 man can finish the work in \( \Large 8 \times 12 \) = 96 days
1 woman can finish the work in \( \Large 4 \times 48 \) = 1 92 days
1 child can finish the work in \( \Large 10 \times 24 \) = 240 days
1 man's 1 day's work = \( \Large \frac{1}{96} \)
1 woman's 1 day's work = \( \Large \frac{1}{192} \)
1 child's 1 day's work = \( \Large \frac{1}{240} \)
(10 men + 4 women + 10 children)'s 1 day's work
= \( \Large \left(\frac{10}{96}+\frac{4}{192}+\frac{10}{240}\right) \)
= \( \Large \left(\frac{5}{48}+\frac{1}{48}+\frac{1}{24}\right) \)
=\( \Large \left(\frac{5+1+2}{48}\right) \)
= \( \Large \frac{8}{48} = \frac{1}{6} \)
Hence, they will finish the work in 6 days.
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