It costs Rs. p to send each of the first 1000 messages and Rs. q to send each message after the first 1000. If r is greater than 1000, what is the total cost in rupees of sending r messages in terms of p, q and r?

Introduction / Context:
This algebraic word problem uses a piecewise pricing scheme. The cost per message changes after a threshold, which is a typical model in telecommunications and bulk pricing scenarios. We must express the total cost symbolically in terms of p, q and r.

Given Data / Assumptions:
- Cost per message for the first 1000 messages = Rs. p.
- Cost per message for each additional message beyond 1000 = Rs. q.
- Total number of messages sent = r, with r greater than 1000.
- We assume the pricing scheme is exactly as stated with no fixed charges.

Concept / Approach:
The total cost is the sum of two parts:
1. Cost of the first 1000 messages.2. Cost of the remaining (r - 1000) messages.
Then we simplify the expression and match it with the given options.

Step-by-Step Solution:
Step 1: Cost of the first 1000 messages = 1000 * p.Step 2: Number of additional messages beyond 1000 = r - 1000.Step 3: Cost of additional messages = (r - 1000) * q.Step 4: Total cost = 1000p + (r - 1000)q.Step 5: Expand (r - 1000)q = rq - 1000q.Step 6: Total cost = 1000p + rq - 1000q.Step 7: Factor 1000 from the first and last terms: 1000p - 1000q = 1000(p - q).Step 8: So total cost = 1000(p - q) + qr.

Verification / Alternative check:
Write the expression as 1000p + (r - 1000)q and check with an example. Suppose p = 2, q = 1 and r = 1500. Then cost should be 1000 * 2 + 500 * 1 = 2000 + 500 = 2500. Using the simplified form 1000(p - q) + qr gives 1000(2 - 1) + 1 * 1500 = 1000 + 1500 = 2500, which matches.

Why Other Options Are Wrong:
- 1000 (r - p) + pq incorrectly treats r - p as a count of messages and pq as an added term.
- 1000p + qr includes all r messages at cost q without subtracting the first 1000 at cost p.
- 1000(r - q) + pr mixes units incorrectly and does not separate the threshold at 1000 messages.

Common Pitfalls:
- Forgetting to subtract 1000 from r for the additional messages.
- Treating p and q as counts instead of rates per message.
- Not simplifying the expression carefully, which can cause a mismatch with the correct option.

Final Answer:
The total cost of sending r messages is 1000(p - q) + qr.