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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

Answer: b
Explanation 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 = $$\frac{1}{{10}}$$
On solving the two equations,
$$x = \frac{{11}}{{400}},\,\,\,y = \frac{1}{{400}}$$
1 woman’s 1 day’s work = $$\frac{1}{{400}}$$
10 women’s 1 day’s work = $$ {\frac{1}{{400}} \times 10} $$   = $$\frac{1}{{40}}$$
10 women will complete the work in 40 days

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