Question: What was the share of the picnic cost to be borne by each student?
Statements:
I) The total cost of the picnic was ₹ 12,500, and the number of students who went for the picnic was 15.
II) If 3 fewer students would have gone, then the cost of the picnic per student would have increased by ₹ 120.
The question asks to determine if the given statements are sufficient to calculate the share of the picnic cost borne by each student.
Statement I Sufficiency Analysis
Statement I provides the total cost of the picnic and the number of students who attended.
- Total Cost = ₹ 12,500
- Number of Students = 15
The cost per student can be calculated by dividing the total cost by the number of students:
Cost per student = Total Cost / Number of Students
Using LaTeX notation: Cost per student = \(\frac{₹ 12,500}{15}\)
This calculation yields a specific value (₹ 833.33). Therefore, Statement I alone is sufficient to answer the question.
Statement II Sufficiency Analysis
Statement II presents a hypothetical scenario where fewer students attended, leading to an increased cost per student.
Let \(C\) be the total cost and \(N\) be the original number of students.
Original cost per student = \(\frac{C}{N}\)
If 3 fewer students attended, the number of students would be \(N-3\). The new cost per student would be \(\frac{C}{N-3}\).
According to the statement, the new cost per student is ₹ 120 more than the original cost per student:
\(\frac{C}{N-3} = \frac{C}{N} + 120\)
This equation has two unknown variables, \(C\) and \(N\). We cannot determine the original cost per student (\(\frac{C}{N}\)) from this single equation without knowing the value of either \(C\) or \(N\). Therefore, Statement II alone is not sufficient.
Conclusion
Statement I provides direct information to calculate the cost per student. Statement II does not provide enough information to calculate the cost per student.
Thus, Statement I alone is sufficient, while Statement II alone is not sufficient.
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