The speed of the stream flow is 1 km/hr. A motor boat travels 35 km upstream and returns to the starting point in 12 hours. What is the speed of the motor boat in still water (in km/hr)?

The correct answer is (B) 6.

• Given: Speed of stream (s) = 1 km/hr. Let the speed of the motor boat in still water be x km/hr. Time taken for the round trip (Total Time) = 12 hours. Distance (d) = 35 km. The formula used is Total Time = [d / (x - s)] + [d / (x + s)].
• Substituting the values: 12 = [35 / (x - 1)] + [35 / (x + 1)]. Simplifying: 12 = 35 * [(x + 1 + x - 1) / (x^2 - 1)] => 12 = 35 * [2x / (x^2 - 1)]. This leads to 12(x^2 - 1) = 70x, or 6x^2 - 35x - 6 = 0. Solving the quadratic equation using the splitting method: 6x^2 - 36x + x - 6 = 0 => 6x(x - 6) + 1(x - 6) = 0. This gives (6x + 1)(x - 6) = 0. Since speed cannot be negative, x = 6 km/hr.
• Verification: If x = 6, upstream speed = 6 - 1 = 5 km/hr, time = 35/5 = 7 hours. Downstream speed = 6 + 1 = 7 km/hr, time = 35/7 = 5 hours. Total time = 7 + 5 = 12 hours. Other options fail to satisfy the total time equation, confirming (B) is the unique correct result.