14 men can do a work in 18 days, 15 women can do the same work in 24 days. If 14 men work for the first 3 days and 10 women work for the next 3 days, find the part of the work left after that.

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**Solution:**

1. Calculate the work done by 14 men in one day:
   - 14 men complete the work in 18 days, so work done by 14 men in one day = $\frac{1}{18}$

2. Work done by 14 men in first 3 days:
   - $3 	imes \frac{1}{18} = \frac{1}{6}$

3. Calculate the work done by 15 women in one day:
   - 15 women complete the work in 24 days, so work done by 15 women in one day = $\frac{1}{24}$

4. Work done by 10 women in one day:
   - Work done by 1 woman in one day = $\frac{1}{24 	imes 15} = \frac{1}{360}$
   - Work done by 10 women in one day = $10 	imes \frac{1}{360} = \frac{1}{36}$

5. Work done by 10 women in next 3 days:
   - $3 	imes \frac{1}{36} = \frac{1}{12}$

6. Total work done in 6 days:
   - $\frac{1}{6} + \frac{1}{12} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4}$

7. Remaining work:
   - $1 - \frac{1}{4} = \frac{3}{4}$

**Answer:** $\frac{3}{4}$

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