Watches are bought at prices ranging from Rs. 200 to Rs. 350 and sold at prices ranging from Rs. 300 to Rs. 425. What is the greatest possible total profit in rupees that can be made by selling nine watches under these conditions?

Introduction / Context:
This question is about maximizing profit when there is a permitted range for buying and selling prices. It is a simple optimization problem that does not require percentages. Instead, we use the idea that maximum profit is obtained by buying at the lowest possible cost and selling at the highest possible price within the given ranges for each item.

Given Data / Assumptions:

• Each watch can be bought for any price between Rs. 200 and Rs. 350.
• Each watch can be sold for any price between Rs. 300 and Rs. 425.
• There are nine watches in total.
• We assume that it is possible to buy each watch at the minimum allowed cost and sell each at the maximum allowed price.
• We must find the maximum total profit over all nine watches.

Concept / Approach:
To maximize profit, the trader must minimize cost and maximize selling price per watch. Therefore, he will buy each watch at the lowest price in the allowed range and sell each at the highest price in the allowed range. The profit per watch will be the difference between the highest selling price and the lowest cost price. The total profit is then this difference multiplied by the total number of watches, which is nine.

Step-by-Step Solution:
Minimum possible cost price per watch equals 200 rupees.Maximum possible selling price per watch equals 425 rupees.Maximum profit per watch equals 425 minus 200 equals 225 rupees.There are nine watches in total.Therefore, maximum total profit equals 225 multiplied by 9.225 * 9 equals 2025 rupees.

Verification / Alternative check:
We can verify logically that there is no better strategy. Any increase in cost above 200 rupees reduces profit directly. Any decrease in selling price below 425 rupees also reduces profit. Since the ranges are inclusive and we are allowed to choose any value within them, taking the extremes gives the maximum difference between selling price and cost price. Multiplying that difference by the number of identical items gives the maximum total profit.

Why Other Options Are Wrong:
Option 1800 rupees corresponds to a smaller per watch profit and would assume either a higher cost price than 200 or a lower selling price than 425. Option 2000 rupees is not an exact multiple of 9 given the 225 rupee per watch gap, and does not match the precise calculation. Option 1750 rupees also does not correspond to any consistent choice of minimum cost and maximum selling price. Only 2025 rupees matches the optimal difference multiplied by nine watches.

Common Pitfalls:
Some learners mistakenly average the buying and selling ranges and multiply the difference of averages by nine, which gives a smaller profit. Others assume the same fixed price for all watches without using the extremes of the range. Always remember that when the goal is to maximize profit under such flexible conditions, the best strategy is to buy as low as allowed and sell as high as allowed for every item.

Final Answer:
The greatest possible total profit on nine watches is Rs. 2025.