1. **Problem statement:** A can complete a work in 20 days, B can complete the same work in 30 days. They work together for 5 days, then A leaves. We need to find how many more days B will take to finish the remaining work. 2. **Formula and rules:** - Work done = Rate × Time - Rate of A = $\frac{1}{20}$ work/day - Rate of B = $\frac{1}{30}$ work/day - When working together, their combined rate = $\frac{1}{20} + \frac{1}{30}$ 3. **Calculate combined rate:** $$\frac{1}{20} + \frac{1}{30} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12}$$ So, together they complete $\frac{1}{12}$ of the work per day. 4. **Work done in 5 days together:** $$5 \times \frac{1}{12} = \frac{5}{12}$$ 5. **Remaining work:** $$1 - \frac{5}{12} = \frac{12}{12} - \frac{5}{12} = \frac{7}{12}$$ 6. **B's rate:** $$\frac{1}{30}$$ work per day. 7. **Time for B to finish remaining work:** $$\text{Time} = \frac{\text{Remaining work}}{\text{B's rate}} = \frac{\frac{7}{12}}{\frac{1}{30}} = \frac{7}{12} \times 30 = \frac{7 \times 30}{12}$$ 8. **Simplify:** $$\frac{7 \times \cancel{30}}{\cancel{12}} = \frac{7 \times 5}{2} = \frac{35}{2} = 17.5$$ 9. **Answer:** B will take 17.5 days to finish the remaining work, which is closest to option (D) 18 days. **Final answer:** 18 days