Question

A boy throws stones one by one where the distance to which a boy can throw the stone is inversely proportional to its weight. He breaks the stone into 3 pieces whose weights are in the ratio 1 : 3 : 2. Upto what distance can he throw the unbroken stone?
Statement 1: the sum of the distances covered by the three broken pieces is 22 m
Statement 2: the total weight of the unbroken stone is 12 kg

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

Answer: (E)

To solve the given problem, we need to understand the relationship between the distance a stone can be thrown and its weight. According to the problem, the distance is inversely proportional to the weight of the stone. 

The stone is broken into three pieces with weights in the ratio \(1 : 3 : 2\). This means if the total weight of the stone is \(w\), the weights of the individual pieces are \(w_1 = \frac{w}{6}\), \(w_2 = \frac{3w}{6} = \frac{w}{2}\), and \(w_3 = \frac{2w}{6} = \frac{w}{3}\).

From the problem, we have:

1. Statement 1: The sum of the distances covered by the three broken pieces is 22 m.
2. Statement 2: The total weight of the unbroken stone is 12 kg.

 

The question asks how far the unbroken stone can be thrown. Let's analyze the statements:

From Statement 1:

\(d_1 + d_2 + d_3 = 22 \text{m}\), where \(d_i \propto \frac{1}{w_i}\). Therefore, we establish that:

• \(d_1 \propto \frac{1}{w/6}\)
• \(d_2 \propto \frac{1}{w/2}\)
• \(d_3 \propto \frac{1}{w/3}\)

With this information, we cannot determine the value of \(w\), nor find the exact distance the unbroken stone can be thrown.

From Statement 2:

The total weight \(w = 12 \text{kg}\). This gives us the weights of individual broken pieces but does not tell us the distance each piece is thrown. Hence, we do not have enough information about the distances.

Analyzing both statements together:

Even when combining both statements, we do not have sufficient data to find the individual distances \(d_1\), \(d_2\), and \(d_3\). Without knowing or assuming a constant of proportionality, the actual distance the unbroken stone can be thrown remains undetermined.

Conclusion: Neither Statement 1 nor Statement 2 alone, nor the two together, suffices to answer the question about the distance the unbroken stone can be thrown. Therefore, the correct answer is:

Neither statement (1) nor statement (2) suffices to answer the question