Nine students of a class contribute money towards a charity fund. Seven of them give Rs. 50 each and the other two give, respectively, Rs. 50 and Rs. 90 more than the others. What is the average contribution (in rupees) of the nine students?

Introduction / Context:
This question is a straightforward application of averages and total contributions in a small group. We know how much most of the students give and how much extra the remaining students contribute. From this, we can compute the total contribution and then the average per student.

Given Data / Assumptions:

• Total number of students contributing = 9.
• Seven students each contribute Rs. 50.
• One of the remaining two contributes Rs. 50 more than the others, that is 50 + 50 = Rs. 100.
• The other contributes Rs. 90 more than the others, that is 50 + 90 = Rs. 140.
• We assume all contributions are in rupees and made once.

Concept / Approach:
The basic idea is: Average contribution = total contribution / number of students. So we first calculate the total contribution by summing the amounts from each category of students and then divide by 9 to obtain the average contribution per student.

Step-by-Step Solution:
Step 1: Compute total contribution of the 7 students who each give Rs. 50. Contribution of 7 students = 7 * 50 = Rs. 350. Step 2: Compute contribution of the student who gives Rs. 50 more than the others. That student gives = 50 + 50 = Rs. 100. Step 3: Compute contribution of the student who gives Rs. 90 more than the others. That student gives = 50 + 90 = Rs. 140. Step 4: Compute total contribution of all 9 students. Total = 350 + 100 + 140 = Rs. 590. Step 5: Compute the average contribution. Average = 590 / 9 ≈ 65.555..., which we round to Rs. 65.56.

Verification / Alternative check:
We can approximate to check reasonableness. If all 9 students had given Rs. 65 each, the total would be 9 * 65 = Rs. 585. Here the actual total is Rs. 590, which is slightly more, so the average should be slightly more than 65, around 65.5. This matches our exact value of approximately Rs. 65.56.

Why Other Options Are Wrong:
An average of Rs. 60 would give a total of 9 * 60 = Rs. 540, which is less than the known total of Rs. 590. An average of Rs. 70 would give a total of 630, which is too high. An average of Rs. 75 would give a total of 675, far above the actual sum. Only Rs. 65.56 corresponds correctly to the actual total of Rs. 590 and the given contributions.

Common Pitfalls:
A common error is misreading the phrase more than the others and adding 50 and 90 directly to 0 instead of to 50. Another mistake is to try to average the different contribution amounts directly without computing the total. Always sum contributions correctly and then divide by the total number of contributors to find the average.

Final Answer:
The average contribution of the nine students is approximately Rs. 65.56 per student.