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1. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

A. 35

B. 40

C. 45

D. 50

Solution:

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y
Then, 4x + 6y =

\frac{1}{8}

and 3x + 7y =

\frac{1}{10}

Solving the two equations, we get

x = \frac{11}{400}, y = \frac{1}{400}

∴ 1 woman's 1 day's work =

\frac{1}{400}

⇒ 10 women's 1 day's work =

\frac{1}{400} \times 10

\frac{1}{40}

Hence, 10 women will complete the work in 40 days

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