The stream flows at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat (in kmph) in still water is

The correct answer is (B) 6.

• Given: Speed of stream (v) = 1 kmph. Distance (d) = 35 km. Total time (T) = 12 hours. Let the speed of the motor boat in still water be x kmph. The speed upstream is (x - 1) and downstream is (x + 1). The formula is T = d/(x - 1) + d/(x + 1).
• Step-by-step: 12 = 35/(x - 1) + 35/(x + 1). Dividing by 7: 12/7 = 1/(x - 1) + 1/(x + 1). Simplifying: 12/7 = (x + 1 + x - 1) / (x^2 - 1) = 2x / (x^2 - 1). Cross-multiply: 12(x^2 - 1) = 14x. Dividing by 2: 6x^2 - 6 = 7x. Rearranging: 6x^2 - 7x - 6 = 0. Solving the quadratic equation: 6x^2 - 9x + 4x - 6 = 0, which gives (3x + 2)(2x - 3) = 0. Alternatively, factorizing: 6x^2 - 9x + 4x - 6 = 0 implies (2x - 3)(3x + 2) = 0 is incorrect; standard quadratic formula yields (6x+4)(x-1.5) or checking options: if x=6, 35/5 + 35/7 = 7 + 5 = 12 hours.
• Verification: Substituting x = 6, 35/5 + 35/7 = 7 + 5 = 12. Other options fail: for 8, 35/7 + 35/9 is not 12. Thus, 6 kmph is the only correct speed.