14 men can complete a work in 18 days, and 21 women can complete the same work in 20 days. If a child is 20\% less efficient than a man, how many days will 15 children working together take to finish the work?

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**Solution:**

1. Calculate the work done by one man in one day:
   - Total work = 1 unit
   - 14 men complete work in 18 days, so work done by 14 men in one day = $ $\frac{1}{18}$ $
   - Work done by 1 man in one day = $ $\frac{1}{18 \times 14} = \frac{1}{252}$ $

2. Efficiency of one child:
   - A child is 20\% less efficient than a man, so efficiency of child = 80\% of man's efficiency
   - Work done by one child in one day = $ $0.8 \times \frac{1}{252} = \frac{0.8}{252} = \frac{2}{630}$ $

3. Work done by 15 children in one day:
   - $ $15 \times \frac{2}{630} = \frac{30}{630} = \frac{1}{21}$ $

4. Time taken by 15 children to complete the work:
   - Since they complete $ $\frac{1}{21}$ $ of work in one day, total time = 21 days

**Answer:** 21 days

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