Question:medium

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

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
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The Correct Option is

Solution and Explanation

The correct answer is option (E):
Neither statement (1) nor statement (2) suffices to answer the question

Here's a breakdown of why the answer "Neither statement (1) nor statement (2) suffices to answer the question" is correct, along with an educational explanation:

The core concept is inverse proportionality. If distance (d) is inversely proportional to weight (w), this means d = k/w, where k is a constant of proportionality. This constant tells us the relationship strength between weight and distance.

Let's analyze the statements:

Statement 1: The sum of the distances covered by the three broken pieces is 22 m.

* This statement gives us information about the broken pieces. Let the weights of the broken pieces be w, 3w, and 2w. Their respective distances thrown would be d1 = k/w, d2 = k/3w, and d3 = k/2w. We know that d1 + d2 + d3 = 22. This translates to k/w + k/3w + k/2w = 22. We can simplify to (6k + 2k + 3k) / 6w = 22, so 11k/6w = 22. We can determine k/w but we don't know the weight of the original stone. We need to find the distance thrown by the unbroken stone, which would have a weight of w + 3w + 2w = 6w. To do this we would need to know k and w. We are only able to determine k/w. Therefore, statement 1 alone isn't enough.

Statement 2: The total weight of the unbroken stone is 12 kg.

* This tells us the combined weight of the broken pieces is 12 kg. We know that the weights of the broken pieces add up to 12 kg. This provides no information about the distance covered by the broken pieces. We would need to know the original distance constant k to determine the distances. Therefore, statement 2 alone isn't enough.

Combining the statements:

* If we knew the total weight, we would then know that the combined weights is 12kg which would mean 6w=12 kg. Solving would give w = 2kg. We could determine the weight of each individual piece (2kg, 6kg and 4kg).
* From statement 1, we could determine that 11k/6w = 22. We could substitute the value of w we determined to determine the constant k. Knowing the k constant and total weight of the original stone we can determine the distance of the throw.

* Because the two pieces of information don't have a shared variable, the two statements do not allow us to determine the answer.

Since neither statement alone, nor the combination of both, provides enough information to determine the throwing distance of the unbroken stone, the correct answer is that neither statement is sufficient. We need both the total weight and some information about the distances of the broken pieces to solve the problem.
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