A cyclist rides from his village to town at 16 km/h and returns at 12 km/h. If the entire journey takes 7 hours, what is the distance from the village to the town? MCQ with Answer and Explanation
A cyclist rides from his village to town at 16 km/h and returns at 12 km/h. If the entire journey takes 7 hours, what is the distance from the village to the town?
A. 45 km
B. 54 km
C. 48 km
D. 42 km
Answer: Option C
Solution (By JKSSB Mock Tests)
Let distance be d. d/16 + d/12 = 7 => (3d + 4d) / 48 = 7 => 7d / 48 = 7 => d = 48 km.
A boat goes 6 km upstream and returns back to the starting point in 2 hours. If the speed of the stream is 4 km/h, find the speed of the boat in still water.
Explanation:
Let speed of boat in still water be v. 6 / (v - 4) + 6 / (v + 4) = 2 => 3 / (v - 4) + 3 / (v + 4) = 1 => 3(v + 4 + v - 4) = v^2 - 16 => 6v = v^2 - 16 => v^2 - 6v - 16 = 0. Solving the quadratic equation gives (v - 8)(v + 2) = 0. Since speed must be positive, v = 8 km/h.
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