Three students A, B, and C hire a computer for a month. Usage is proportional to (number of floppies run) × (number of days). A runs 27 floppies for 19 days, B runs 21 for 17 days, and C runs 24 for 23 days. If the rent is ₹ 23,700, how much should A pay?

Introduction / Context:
Cost-sharing by usage typically uses a proportional metric. Here, the metric is (floppies run) × (days). Each student’s share equals total rent multiplied by his usage fraction over total usage.

Given Data / Assumptions:

• A-usage = 27 × 19
• B-usage = 21 × 17
• C-usage = 24 × 23
• Total rent = ₹ 23,700

Concept / Approach:
Compute each usage, sum them, form A’s fraction, and multiply by the total rent. Simplify ratios where possible to minimize arithmetic.

Step-by-Step Solution:
A = 27*19 = 513B = 21*17 = 357C = 24*23 = 552Total usage = 513 + 357 + 552 = 1422A’s share = 23700 * (513 / 1422)Reduce: 23700/1422 = 3950/237 and 513/237 = 171/79Hence A’s share = (171/79)*3950 = 50*171 = ₹ 8550

Verification / Alternative check:
Compute B and C similarly; the three shares will sum to ₹ 23,700, confirming proportional division.

Why Other Options Are Wrong:
Only ₹ 8550 matches the exact proportional calculation; others deviate from the correct fraction 513/1422.

Common Pitfalls:
Adding floppies and days instead of multiplying; forgetting to use exact arithmetic leading to rounding errors in large numbers.

Final Answer:
₹ 8550