Multiple choice

The ratio of the speed of a boat in the still water and the speed of the stream is 7 : 5. The ratio of the speed of the stream to the speed of another boat in still water is 6 : 8. What is the ratio of the speed of the first boat to that of the second boat in still water?

  1. 19 : 20

  2. 20 : 21

  3. 21 : 20

  4. 23 : 21

  5. 25 : 23
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C Correct answer
Explanation

Let v1, v2 be boat speeds and s be stream speed. v1/s = 7/5. s/v2 = 6/8 = 3/4. We want v1/v2. v1 = (7/5)s. v2 = (4/3)s. v1/v2 = (7/5) / (4/3) = 21/20.

AI explanation

To make the stream speed equivalent in both ratios, multiply the first ratio (7 : 5) by 6 to get 42 : 30, and write the second ratio (6 : 8) as 30 : 40. The speed ratio of the first boat to the second boat in still water then becomes 42 : 40, which simplifies to 21 : 20.

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