4 men and 6 women can complete a job in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women take to complete the same job?

Let 1 man's work per day = $M$ (fraction of job completed in 1 day)

Let 1 woman's work per day = $W$ (fraction of job completed in 1 day)

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4 men and 6 women complete the job in 8 days.

Work done per day by this group = $4M + 6W$

In 8 days they complete the full job:

$8(4M + 6W) = 1$

$32M + 48W = 1$ ... (Equation 1)

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3 men and 7 women complete the job in 10 days.

Work done per day by this group = $3M + 7W$

In 10 days they complete the full job:

$10(3M + 7W) = 1$

$30M + 70W = 1$ ... (Equation 2)

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From the two equations:

$32M + 48W = 1$ ... (1)

$30M + 70W = 1$ ... (2)

Multiply equation (1) by 30:

$960M + 1440W = 30$

Multiply equation (2) by 32:

$960M + 2240W = 32$

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$960M + 2240W = 32$

$960M + 1440W = 30$

Subtracting:

$800W = 2$

$W = \dfrac{2}{800}$

$W = \dfrac{1}{400}$

1 woman completes $\dfrac{1}{400}$ of the job per day.

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10 women working together complete:

$10 \times \dfrac{1}{400} = \dfrac{10}{400} = \dfrac{1}{40}$ of the job per day

Time to complete the full job:

$\text{Time} = 1 \div \dfrac{1}{40}$

$\text{Time} = 40$ days

Therefore, 10 women will take 40 days to complete the job.