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 given data and statements. From statement I: - The ground dimensions are 80m × 50m. - This determines the positions of Raju and Ratan at the mid-points of the shorter sides (at (25, 0) and (25, 80), respectively).

From statement II: - The area of the triangle formed by Raju, Rivu, and Ratan is 1,000 square metres. - Using the formula for the area of a triangle:

Area \(= \frac{1}{2} \times \text{base} \times \text{height},\)

where the base is the distance between Raju and Ratan (80m), we can find Rivu's coordinates.

Step 2: Calculate the time taken. The speed of the ball is constant at 10m/s. Using the coordinates of Rivu, the distances between Raju, Rivu, and Ratan can be determined, and hence the total time can be calculated:

Time \(= \frac{\text{Total Distance}}{\text{Speed}} + \text{Holding Time.}\)

Both statements I and II are necessary to calculate the total distance and time.

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