1. **State the problem:** The ratio of female to male employees is initially 2:5. After hiring 6 more women, the ratio becomes 7:10. We need to find the total number of employees after hiring these 6 women. 2. **Set variables:** Let the initial number of females be $2x$ and males be $5x$. 3. **After hiring 6 women:** Females become $2x + 6$, males remain $5x$. 4. **Use the new ratio:** $$\frac{2x + 6}{5x} = \frac{7}{10}$$ 5. **Cross multiply:** $$10(2x + 6) = 7(5x)$$ 6. **Expand:** $$20x + 60 = 35x$$ 7. **Rearrange:** $$60 = 35x - 20x$$ 8. **Simplify:** $$60 = 15x$$ 9. **Solve for $x$:** $$x = \frac{60}{15} = 4$$ 10. **Calculate total employees after hiring:** Females = $2x + 6 = 2(4) + 6 = 8 + 6 = 14$ Males = $5x = 5(4) = 20$ Total = $14 + 20 = 34$ **Final answer:** 34 persons are employed after hiring the 6 women.