Multiple choice

Given below are two statements based on the following: A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Statement I: Speed of the boat in still water is 12 km per hour. Statement II: Speed of the stream is 4 km per hour. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true but Statement II is false.

  4. Statement I is false but Statement II is true.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let u be upstream speed and v be downstream speed. 30/u + 28/v = 7 and 21/u + 21/v = 5. Solving this system yields u = 6 and v = 14. Boat speed = (14+6)/2 = 10 km/hr. Stream speed = (14-6)/2 = 4 km/hr. Statement I (12 km/hr) is false, Statement II (4 km/hr) is true.

AI explanation

Assume the speed of the boat in still water is U and the speed of the stream is V. From the given conditions, 30 divided by (U minus V) plus 28 divided by (U plus V) equals 7, and 21 divided by (U minus V) plus 21 divided by (U plus V) equals 5. Solving this system of equations yields U equals 10 and V equals 4, meaning Statement I is false but Statement II is true.

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