A) 9.4 kmph
B) 10.2 kmph
C) 9.6 kmph
D) 9.8 kmph
E) 8.7 kmph
Correct Answer: C
Solution :
Let the distance be D km. (Difference in lime = 12 : 30 - 10 : 30 = 2 hrs) Now,\[\frac{\text{D}}{\text{8}}\text{-}\frac{\text{D}}{\text{12}}\text{=2}\] \[\therefore \text{D=48 km}\] So, he started the journey at (12 : 30 ? 6 =) 6 : 30 am. Now, to get there at 11 : 30 am he must cycle at \[\frac{48}{5}\text{=9}\text{.6 kmph}\] Quicker Approach; He has to reach exactly between 10 : 30 am and 12 : 30 pm (ie at 11 : 30 am) \[\Rightarrow \] He should take average of the two times taken by him with 8 km/hr and 12 km/hr \[\Rightarrow \] He should cycle at the average speed of the two speeds (8.km/hr & 12 km/hr) during both journey of equal distances. So, reqd speed\[=\frac{2\times 8\times 12}{8+12}=\frac{2\times 8\times 12}{20}\] \[=\frac{96}{10}=9.6\text{ km/hr}\]
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