Multiple choice

A boat starts from A and move towards B. Another boat from B, with the same velocity as that of first boat, starts moving towards A. They meet at a point which is 10 km towards B from exactly half way from A to B and the distance between A and B is 60 km. What is the ratio of speed of boat to that of water?

  1. 2 : 1

  2. 3 : 2

  3. 3 : 1

  4. 4 : 1

  5. 5 : 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Distance = 60 km. Midpoint = 30 km. Meeting point is 10 km towards B from midpoint, so 40 km from A and 20 km from B. Boat 1 travels 40 km downstream, Boat 2 travels 20 km upstream. Let v be boat speed, u be water speed. Time taken is equal: 40/(v+u) = 20/(v-u). 2(v-u) = v+u => 2v - 2u = v + u => v = 3u. Ratio v:u = 3:1.

AI explanation

The halfway point is 30 km from both A and B, and the meeting point is 10 km towards B from the halfway point, making the meeting point 40 km from A and 20 km from B. Since the boats start at the same time, the ratio of their effective speeds is the ratio of the distances they cover: 40:20, or 2:1. Let the speed of both boats be b and the speed of the water be w; the boat from A goes downstream at speed b plus w, and the boat from B goes upstream at speed b minus w. From the ratio, b plus w equals 2 times (b minus w), which expands to b plus w equals 2b minus 2w, meaning b equals 3w. The ratio of the speed of the boat to the speed of the water is 3:1.

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