A supplier sells a set of cartridges to a newspaper publishing house for Rs. 1540 and earns a profit of 25 percent on the deal. What is the cost price of the cartridges for the supplier?

Introduction / Context:
This is a direct profit percentage problem. The selling price and profit percent are known, and we need to find the cost price. Such questions test basic rearrangement of the profit formula and are frequently asked in entry level quantitative aptitude tests.

Given Data / Assumptions:

• Selling price (SP) of the cartridges = Rs. 1540.
• Profit percentage = 25 percent.
• We must find the cost price (CP) for the supplier.

Concept / Approach:
Profit percent is defined as profit divided by cost price, multiplied by 100. When profit percent and selling price are known, we use the relationship SP = CP * (1 + profit percent / 100). Rearranging that gives CP = SP / (1 + profit percent / 100). This formula is the easiest way to move from selling price and profit percent back to cost price.

Step-by-Step Solution:
Let CP be the cost price. Given profit percent = 25 percent, so SP = CP * (1 + 25 / 100) = CP * 1.25. We know SP = 1540, so 1540 = 1.25 * CP. Therefore CP = 1540 / 1.25. Compute CP = 1540 / 1.25 = 1232 rupees.

Verification / Alternative check:
Check using CP = Rs. 1232. Profit at 25 percent = 1232 * 25 / 100 = 308 rupees. Selling price = CP + profit = 1232 + 308 = 1540 rupees. This matches the given selling price, so CP is correctly found.

Why Other Options Are Wrong:
Rs. 1100, Rs. 1440, and Rs. 1793.4: None of these values, when marked up by 25 percent, yield a selling price of 1540 rupees. These options reflect errors in dividing or misapplying the profit percentage formula.

Common Pitfalls:
Some candidates mistakenly compute profit as a percentage of selling price or directly multiply selling price by 0.75 instead of dividing by 1.25. While multiplying by 0.8 would be correct for 25 percent discount, for profit calculation from selling price you must divide by 1 plus the profit rate, not subtract the rate from 1.

Final Answer:
The cost price of the cartridges is Rs. 1232.