Multiple choice

Given below are two statements based on the following: Aman takes half time in rowing a certain distance downstream than upstream. Statement (I): Ratio of the speed of the boat in still water to the speed of the water current is 2 : 1. Statement (II): If the speed of the boat in still water is 6 km per hour, then the speed of the water current is 2 km per hour. In light of the above statements, choose the most appropriate 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 boat speed be B and current be C. Downstream time = D / (B+C), Upstream time = D / (B-C). Given D / (B+C) = 0.5 * (D / (B-C)), so 2(B-C) = B+C, which means B = 3C. Statement I says B:C = 2:1, which is false. Statement II says if B=6, C=2, then B=3C, which is true.

AI explanation

Because Aman takes half the time downstream, his downstream speed must be double his upstream speed. Letting the boat's speed in still water be b and the current be c, this relationship gives us (b + c) equals 2 multiplied by (b minus c). Solving this equation yields b equals 3c, meaning the true ratio of the speed of the boat to the current is 3 : 1, so Statement (I) is false. Using this true ratio, if the boat's speed is 6 km/hr, the current's speed is 2 km/hr, making Statement (II) true. Therefore, Statement (I) is false but Statement (II) is true.

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