Multiple choice

A motor boat named "Destiny" goes downstream from point A to point B and returns immediately. The distance from A to B is equal to the distance travelled by a person at 6 km/hr in 20 hours. It takes the boat 15 hours to complete the whole trip. If the speed of the river were twice, then "Destiny" would took 24 hours to complete the downstream and upstream trip. Which of the following can be obtained from the above given information? (i) Speed of the stream (ii) Speed of "Destiny" in still water (iii) Distance covered by "Destiny" in still water in 10 hours (iv) Time taken by "Destiny" to cover the distance of 216 km in still water

  1. Only (i)

  2. Only (i) and (ii)

  3. Only (iii) and (ii)

  4. All (i), (ii), (iii) and (iv)

  5. Only (i), (ii) and (iv)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The distance AB is 6 * 20 = 120 km. Let boat speed be u, stream speed v. 120/(u+v) + 120/(u-v) = 15. With 2v: 120/(u+2v) + 120/(u-2v) = 24. These equations allow solving for u and v, and subsequently answering all parts.

AI explanation

The distance from A to B is 6 km/hr multiplied by 20 hours equals 120 km. Let the speed of the boat be B and the stream be S. The first condition gives the equation 120 divided by (B plus S) plus 120 divided by (B minus S) equals 15. The second condition gives 120 divided by (B plus 2S) plus 120 divided by (B minus 2S) equals 24. Since we have two distinct equations with two variables, we can uniquely solve for both the speed of the boat in still water and the speed of the stream. Once these speeds are known, the distance covered by the boat in still water in 10 hours and the time taken to cover 216 km in still water can also be calculated. Therefore, all four values can be obtained.

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