Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. Stream is flowing with speed 12 km/hr. Boat A covers 4 km more downstream distance in one hour than boat C in same time period. Distance between two points X and Y is 380 km which is double the distance between X and Z. What is the speed of Boat B in still water? Statement I: Difference between upstream speed of boat A and downstream speed of boat B is 2 km/hr less than the difference between downstream speed of boat A and upstream speed of boat C. Statement II: Boat A covered the distance between point X to Z in 5 hours while moving downstream. Upstream speed of boat B and C are in the ratio 8: 5 respectively. Statement III: Sum of time taken by boat B to cover the distance between point X and Z while travelling upstream and the time taken by boat A to cover the distance between point X and Y while travelling downstream is 21.875 hours.

  1. Only statement I and III together are sufficient

  2. Either statement II and III together are sufficient or statement I alone is sufficient.

  3. Any of the two statements together are sufficient.

  4. Either statement I and III together are sufficient or statement II alone is sufficient.

  5. All statements I, II and III together are sufficient.

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement II alone provides complete information: stream speed (12 km/hr), downstream distance XZ (derived from XY=380km and XY=2×XZ, so XZ=190km), and time for A to cover XZ downstream (5 hours). From this, we find A's downstream speed, then its still water speed. The upstream speed ratio (B:C = 8:5) with the stream speed known allows solving B's still water speed. Statements I and III together also provide sufficient equations through the complex relationships between boats' speeds.