1. **State the problem:** We have a factory with male and female workers. The number of female workers is $\frac{4}{7}$ of the number of male workers. 2. **Define variables:** Let the number of male workers be $M$. Then the number of female workers is $F = \frac{4}{7}M$. 3. **Resignations:** 20% of female workers resigned, so the number of female workers who resigned is $0.20F$. 25% of male workers resigned, so the number of male workers who resigned is $0.25M$. 4. **Total resignations:** The total number of workers who resigned is 62, so: $$0.20F + 0.25M = 62$$ 5. **Substitute $F$:** $$0.20 \times \frac{4}{7}M + 0.25M = 62$$ 6. **Simplify:** $$\frac{0.20 \times 4}{7}M + 0.25M = 62$$ $$\frac{0.8}{7}M + 0.25M = 62$$ 7. **Find common denominator and combine:** $$\frac{0.8}{7}M + \frac{0.25 \times 7}{7}M = 62$$ $$\frac{0.8 + 1.75}{7}M = 62$$ $$\frac{2.55}{7}M = 62$$ 8. **Solve for $M$:** $$M = \frac{62 \times 7}{2.55}$$ 9. **Calculate $M$:** $$M = \frac{434}{2.55} \approx 170.2$$ Since number of workers must be whole, $M = 170$ (assuming rounding). 10. **Calculate $F$:** $$F = \frac{4}{7} \times 170 = 4 \times 24.2857 = 97.14 \approx 97$$ 11. **Find the difference between initial male and female workers:** $$M - F = 170 - 97 = 73$$ **Final answer:** The difference between the initial number of male and female workers is **73**.