10 men and 8 women can do a piece of work in 7
2
1
​
days whereas 6 men and 9 women can do the same work in 10 days. In how many days will 35 women complete the same work?

Let the efficiency of a man be M and a woman be W.
The total work is equal in both cases:

Total Work=(10M+8W)×7.5=(6M+9W)×10
Equating the two expressions:

(10M+8W)×
2
15
​
=(6M+9W)×10
(10M+8W)×3=(6M+9W)×4
30M+24W=24M+36W
30M−24M=36W−24W
6M=12W⟹1M=2W
Now substitute 1M=2W to find the total work in terms of women:

Total Work=(6M+9W)×10=(6(2W)+9W)×10=(12W+9W)×10=21W×10=210W
Let the time taken by 35 women to complete the work be D days:

35W×D=210W
D=
35
210
​
=6 days