Difficulty: Medium
Correct Answer: 77
Explanation:
Introduction / Context:
This is an application of basic arithmetic and the concept of square numbers. The collection rule is that each student contributes a number of paise equal to the total number of students in the group. The question asks us to find the group size from the total collection given in rupees.
Given Data / Assumptions:
- Each student contributes paise equal to the number of students in the group.
- Total collection is Rs 59.29.
- 1 rupee = 100 paise.
Concept / Approach:
If there are n students, each contributes n paise. So the total collection in paise is n × n = n². We first convert the rupee amount into paise, then recognize that this total must be a perfect square. Taking the square root gives the number of students.
Step-by-Step Solution:
Step 1: Let the number of students be n.Step 2: Each student contributes n paise, so total collection in paise is n × n = n².Step 3: Convert Rs 59.29 to paise. Since 1 rupee = 100 paise, Rs 59.29 = 59.29 × 100 = 5929 paise.Step 4: Therefore, n² = 5929.Step 5: Find n by taking the square root: n = √5929.Step 6: Check: 77² = 77 × 77 = 5929, so n = 77.
Verification / Alternative check:
You can quickly square 57, 67 and 87 to see that none of these give 5929. Only 77² equals 5929. This confirms that the number of students is 77.
Why Other Options Are Wrong:
57² = 3249, 67² = 4489 and 87² = 7569. None match the total collection in paise (5929). Therefore those options cannot represent the correct group size under the given contribution rule.
Common Pitfalls:
Students sometimes forget to convert rupees into paise and mistakenly set n² equal to 59.29 instead of 5929. Also, miscalculating squares of two digit numbers may lead to wrong conclusions. Using mental math shortcuts or quick multiplication helps verify squares accurately.
Final Answer:
The number of students in the group is 77.
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