1. **State the problem:** The volume $V$ of a gas is inversely proportional to its pressure $P$. If the volume is $360$ cm³ when the pressure is $20$ g/cm³, find the pressure when the volume is $200$ cm³. 2. **Recall inverse variation formula:** If $V$ varies inversely as $P$, then $$V = \frac{k}{P}$$ where $k$ is the constant of variation. 3. **Find constant $k$ using given values:** $$360 = \frac{k}{20} \implies k = 360 \times 20 = 7200$$ 4. **Find pressure $P$ when volume is $200$ cm³:** Using $$200 = \frac{7200}{P}$$ solve for $P$: $$P = \frac{7200}{200} = 36$$ **Answer:** Pressure is $36$ g/cm³ when volume is $200$ cm³. --- 1. **State the problem:** The temperature $T$ set on an induction cooker is inversely proportional to the cooking time $t$ for one-kilogram meat. The temperature is $1200^\circ$C when the cooking time is $20$ minutes. Find the cooking time when the temperature is increased to $1600^\circ$C. 2. **Express inverse variation mathematically:** $$T = \frac{k}{t}$$ where $k$ is constant. 3. **Find constant $k$ using given values:** $$1200 = \frac{k}{20} \implies k = 1200 \times 20 = 24000$$ 4. **Find cooking time $t$ when temperature is $1600$:** $$1600 = \frac{24000}{t} \implies t = \frac{24000}{1600} = 15$$ **Answer:** It will take $15$ minutes to cook the meat at $1600^\circ$C. --- 1. **State the problem:** Travel time $T$ around an island varies inversely as speed $S$ of the bike. It takes $4$ hours at $25$ kph. Find the travel time when speed reduces to $20$ kph. 2. **Write inverse variation formula:** $$T = \frac{k}{S}$$ 3. **Find constant $k$ using given values:** $$4 = \frac{k}{25} \implies k = 4 \times 25 = 100$$ 4. **Find travel time $T$ at speed $20$ kph:** $$T = \frac{100}{20} = 5$$ **Answer:** Travel time is $5$ hours at $20$ kph.