📊 Work and Time Calculation 📊

Let’s analyze the situation:

4 men + 6 women = 1/8 of the work per day (8 days to complete)

3 men + 7 women = 1/10 of the work per day (10 days to complete)

We can set up equations based on the work rates:

Let’s denote the work rate of 1 man as ‘m’ and 1 woman as ‘w’.

4m + 6w = 1/8

3m + 7w = 1/10

To eliminate ‘m’, multiply the first equation by 3 and the second equation by 4:

12m + 18w = 3/8

12m + 28w = 2/5

Now, subtract the first equation from the second equation:

(12m + 28w) – (12m + 18w) = 2/5 – 3/8

10w = (16 – 15) / 40

10w = 1/40

w = 1/400 (work done by 1 woman per day)

Now, find the work rate of 10 women:

10w = 10/400 = 1/40 (work done by 10 women per day)

Time taken by 10 women to complete the work = 1 / (1/40)

= 40 days

🎉 10 women will complete the work in 40 days. 📊