Multiple choice

In a river, the ratio of the speed of the stream and the speed of a boat in still water is 5 : 7. Again, 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? একটি নদীতে স্রোতের বেগ এবং স্থির জলে নৌকার বেগ এর অনুপাত হল 5:7। পুনরায় স্রোতের বেগ এবং অপর একটি নৌকার স্থির জলে বেগের অনুপাত 6:8। তাহলে স্থির জলে প্রথম নৌকা এবং দ্বিতীয় নৌকার বেগের অনুপাত কত

  1. 19 : 17

  2. 27 : 28

  3. 21 : 20

  4. 27 : 29
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C Correct answer
Explanation

Stream speed S. Boat 1 speed B1 = 7/5 * S. Boat 2 speed B2 = 8/6 * S = 4/3 * S. Ratio B1/B2 = (7/5) / (4/3) = 21/20.

AI explanation

To compare the boats, we first equalize the speed of the stream by making the stream value 30 in both ratios, yielding a ratio of stream to first boat of 30:42 and stream to second boat of 30:40. We then directly compare the still water speeds of the first and second boats, giving the ratio 42 to 40. Simplifying this result by dividing by 2 gives the final ratio of the speed of the first boat to the second boat as 21:20.

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