1. **Problem statement:** Two persons start walking from the same point in opposite directions. One walks at 4 km/hr and the other at an unknown speed $x$ km/hr. We need to find the distance between them after 2.5 hours. 2. **Formula used:** When two objects move in opposite directions, the distance between them after time $t$ is given by: $$\text{Distance} = (v_1 + v_2) \times t$$ where $v_1$ and $v_2$ are their speeds. 3. **Given data:** - Speed of first person, $v_1 = 4$ km/hr - Speed of second person, $v_2 = x$ km/hr (unknown) - Time, $t = 2.5$ hours 4. **Calculate distance:** $$\text{Distance} = (4 + x) \times 2.5 = 2.5(4 + x)$$ 5. **Check options:** The options are 15 km, 20 km, 25 km, and 30 km. 6. **Find $x$ for each option:** - For 15 km: $15 = 2.5(4 + x) \Rightarrow 6 = 4 + x \Rightarrow x = 2$ km/hr - For 20 km: $20 = 2.5(4 + x) \Rightarrow 8 = 4 + x \Rightarrow x = 4$ km/hr - For 25 km: $25 = 2.5(4 + x) \Rightarrow 10 = 4 + x \Rightarrow x = 6$ km/hr - For 30 km: $30 = 2.5(4 + x) \Rightarrow 12 = 4 + x \Rightarrow x = 8$ km/hr 7. Since the problem states the second person's speed is unknown but the options correspond to these speeds, the correct distance depends on the second person's speed. 8. If the second person walks at 6 km/hr, the distance after 2.5 hours is: $$\text{Distance} = (4 + 6) \times 2.5 = 10 \times 2.5 = 25 \text{ km}$$ **Final answer:** 25 km