4 men and 6 women can complete a piece of work in 8 days, while 3 men and 7 women can complete the same work in 10 days. In how many days will 10 women, working together, complete the same piece of work?

ATQ,
Let 1 man's 1-day work be m and 1 woman's 1-day work be w.
Work done by 4 men and 6 women in 8 days is equal to work done by 3 men and 7 women in 10 days.
So,
(4m + 6w) × 8 = (3m + 7w) × 10.
Or,
32m + 48w = 30m + 70w.
Or,
32m - 30m = 70w - 48w.
So,
2m = 22w.
So,
1m = 11w.
Total work = (4m + 6w) × 8.
Put m = 11w: Total work = (4 × 11w + 6w) × 8.
Or,
Total work = (44w + 6w) × 8 = 50w × 8 = 400w.
Work to be done by 10 women = 10w.
Time taken = Total work / 1-day work of 10 women.
So,
Time taken = 400w / 10w = 40 days.
Hence,
the correct answer is C.