Question

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 × 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.

• A. I alone is sufficient to solve the problem
• B. II alone is sufficient to solve the problem
• C. Either of I or II, by itself, is sufficient to solve the problem.
• D. I and II both are required to solve the problem.
• E. The problem cannot be solved even with both I and II.

Answer 1

The Correct Option is A

Step 1: Analyze the provided data and statements. Statement I establishes the ground dimensions as 80m × 50m, fixing Raju and Ratan's positions at the midpoints of the shorter sides, specifically at coordinates (25, 0) and (25, 80) respectively. Statement II states that the triangle formed by Raju, Rivu, and Ratan has an area of 1,000 square metres. Employing the triangle area formula, Area \(= \frac{1}{2} \times \text{base} \times \text{height},\) with the base being the 80m distance between Raju and Ratan, Rivu's coordinates can be ascertained.

Step 2: Calculate the time elapsed. The ball maintains a constant speed of 10m/s. Using Rivu's determined coordinates, the distances between Raju, Rivu, and Ratan can be calculated, enabling the computation of the total time. The formula for time is: Time \(= \frac{\text{Total Distance}}{\text{Speed}} + \text{Holding Time.}\) Both statements I and II are essential for determining the total distance and subsequently the time.

Answer: Both statements I and II are required to solve the problem.