4 men can complete a piece of work in 2 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. If 2 men, 4 women and 10 children work together, in how many days can the work be completed?

1 day

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3 days

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2 days

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4 days

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None of these

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Solution

The correct option is A 1 day
1 man can do the work in 8 days.
1 woman can do the work in 16 days.
1 child can do the work in 20 days.
2m + 4w + 10c can do the work in -
$(\frac{2}{8} + \frac{4}{16} + \frac{10}{20}) \times d = 1$
$⟹ (\frac{1}{4} + \frac{1}{4} + \frac{1}{2}) \times d = 1$
$⟹ d = 1$

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4 men can complete a piece of work in 2 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. If 2 men, 4 women and 10 children work together, in how many days can the work be completed?

The correct option is A 1 day1 man can do the work in 8 days. 1 woman can do the work in 16 days. 1 child can do the work in 20 days. 2m + 4w + 10c can do the work in - (28+416+1020)×d = 1 ⟹(14+14+12)×d = 1 ⟹d = 1