1. The problem asks: If A can finish work in $n$ days, what part of work does A finish in 1 day? The formula for work done per day is $\frac{1}{n}$. Answer: b) $\frac{1}{n}$. 2. If an increase in one quantity causes a decrease in the other, the quantities vary inversely. Answer: b) inversely. 3. Speed and time for a fixed distance vary inversely because if speed increases, time decreases. Answer: a) inverse variation. 4. Given $x$ and $y$ vary inversely, and from the table $x=5$ when $y=30$, find $x$ when $y=10$. Inverse variation means $xy = k$ (constant). Calculate $k = 5 \times 30 = 150$. Find $x$ when $y=10$: $x = \frac{k}{y} = \frac{150}{10} = 15$. Answer: c) 15. 5. Speed = 75 km/hr, time = 20 minutes = $\frac{20}{60} = \frac{1}{3}$ hour. Distance = speed $\times$ time = $75 \times \frac{1}{3} = 25$ km. Answer: d) 25 km. 6. Direct proportion: $y = kx$. Given $x=3$, $y=9$, find $k$. $k = \frac{y}{x} = \frac{9}{3} = 3$. Answer: b) 3. 7. Indirect proportion: $y = \frac{k}{x}$. Given $x=4$, $y=2$, find $k$. $k = xy = 4 \times 2 = 8$. Answer: a) 8. 8. Car travels 14 km in 25 minutes. Speed = $\frac{14}{25/60} = \frac{14}{5/12} = 14 \times \frac{12}{5} = 33.6$ km/hr. Distance in 5 hours = speed $\times$ time = $33.6 \times 5 = 168$ km. 9. 15 workers finish in 42 hours. Work is inversely proportional to number of workers for fixed work. Let $x$ be workers needed for 30 hours. $15 \times 42 = x \times 30$ (since total work is constant). $x = \frac{15 \times 42}{30} = 21$ workers. 10. Cost of 16 apples = 160. Cost per apple = $\frac{160}{16} = 10$. Cost of 14 apples = $14 \times 10 = 140$. 11. $x$ varies inversely as $y$: $xy = k$. Given $x=20$, $y=600$, $k = 20 \times 600 = 12000$. Find $y$ when $x=400$: $y = \frac{k}{x} = \frac{12000}{400} = 30$. 12. $x$ varies directly as $y$: $x = ky$. Given $x=80$, $y=160$, $k = \frac{80}{160} = 0.5$. Find $y$ when $x=64$: $y = \frac{x}{k} = \frac{64}{0.5} = 128$. 13. Flour lasts for 300 persons for 42 days. If 15 more people join, total persons = 315. Flour amount is constant, so $300 \times 42 = 315 \times d$ where $d$ is new days. $d = \frac{300 \times 42}{315} = 40$ days. Final answers: 1) b 2) b 3) a 4) c 5) d 6) b 7) a 8) 168 km 9) 21 workers 10) 140 11) 30 12) 128 13) 40 days