Multiple choice

A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per second, and the ball always moves on straight lines along the ground. Consider the following two additional pieces of information: I. The dimension of the ground is 80 metres x 50 metres. II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres. Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option.

  1. I alone is sufficient to solve the problem.

  2. II alone is sufficient to solve the problem.

  3. Either of I or II, by itself, is sufficient to solve the problem.

  4. Both I and II are required to solve the problem.

  5. The problem cannot be solved even with both I and II.
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A Correct answer
AI explanation

Ratan stands at the opposite midpoint of Raju, and if we use statement I, the distance between them is 80 meters because they are on the shorter sides. Let the distance from Raju to Rivu be x and from Rivu to Ratan be y, which form a right-angled triangle where x squared plus y squared equals 80 squared; since the ball travels at 10 meters per second, the total passing time is (x plus y) divided by 10. Using algebraic substitution with the 3-second and 2-second holding times, this information is sufficient to find the total time. Because statement II only gives the triangle area as 1000 square meters without the hypotenuse, it cannot solve the problem, so I alone is sufficient to solve the problem.

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