Multiple choice

A boat takes $4\ hr$ upstream and $2\ hr$ down the stream for covering the same distance. The ratio of velocity of boat to the water in river is

  1. $1 : 3$
  2. $3 : 1$
  3. $1 : \sqrt{3}$
  4. $\sqrt{3} : 1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be b and water speed be w. Distance = (b-w)*4 = (b+w)*2. 4b - 4w = 2b + 2w. 2b = 6w. b/w = 3/1.

AI explanation

Let the distance be D, the velocity of the boat in still water be v, and the velocity of the water be u. The upstream speed is D divided by 4 hours, which equals (v minus u), and the downstream speed is D divided by 2 hours, which equals (v plus u). Dividing the downstream speed equation by the upstream speed equation gives (v plus u) divided by (v minus u) equals 2, which simplifies to v plus u equals 2v minus 2u. Solving this equation gives v equals 3u, so the ratio of the velocity of the boat to the velocity of the water is 3 to 1.

Keep practicing — related questions