A paricular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?

A paricular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?
[A]18 days
[B]9 days
[C]6 days
[D]4 days

4 days
According to the question,
10 men’s one day’s work = \frac{1}{12}
∴ 1 man one day’s work = \frac{1}{12\times 10} = \frac{1}{120}
Similarly,
1 woman one day’s work = \frac{1}{6\times 10} = \frac{1}{60}
∴ (1 man + 1 woman)’s one day’s work =  \frac{1}{120}+\frac{1}{60}
= \frac{1+2}{120} = \frac{3}{120} = \frac{1}{40}
∴ (10 man + 10 woman)’s one day’s work =  \frac{10}{40} = \frac{1}{4}
Therefore, both the team can finish the whole work in 4 days.
Hence option [D] is the right answer.

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