A college bag is sold for Rs 1,540. The cost price of the bag is 240% more than the profit obtained on it at this selling price. What is the cost price of the college bag?

Introduction / Context:
This profit and loss question expresses the relationship between cost price and profit using a percentage comparison, rather than giving a direct profit percentage. The cost price is said to be 240% more than the profit amount. From the selling price and this relationship, we must find the cost price. Problems like this test your ability to convert percentage comparisons between profit and cost into algebraic equations.

Given Data / Assumptions:

• Selling price (SP) of the college bag = Rs 1,540.
• Cost price (CP) is 240% more than the profit.
• If profit is P, then CP = P + 240% of P.
• We assume no extra charges or hidden costs.
• We need to determine CP.

Concept / Approach:
Let the profit be P. Saying that the cost price is 240% more than the profit means CP = P + 2.4P = 3.4P. Since selling price equals cost price plus profit, SP = CP + P. Substituting CP = 3.4P into SP = CP + P gives SP = 4.4P. With a known SP of 1,540, we can solve for P and then find CP. This method is a straightforward application of algebra and percentage increase relationships.

Step-by-Step Solution:
Step 1: Let profit = P.Step 2: Cost price is 240% more than profit, so CP = P + 2.4P = 3.4P.Step 3: Selling price SP = CP + P = 3.4P + P = 4.4P.Step 4: Given SP = 1,540, so 4.4P = 1,540.Step 5: P = 1,540 / 4.4 = 350.Step 6: Therefore CP = 3.4P = 3.4 * 350 = 1,190.

Verification / Alternative check:
Consider CP = Rs 1,190 and profit = Rs 350. The statement says that CP is 240% more than profit. Check: 240% of 350 = 2.4 * 350 = 840. Then profit plus this extra 240% is 350 + 840 = 1,190, which matches CP. Also, SP = CP + profit = 1,190 + 350 = 1,540, exactly the given selling price. Both conditions are satisfied, confirming our calculation.

Why Other Options Are Wrong:
Other values such as Rs 1,288, Rs 1,365 and Rs 1,452 do not simultaneously satisfy SP = CP + profit and the ratio CP = P + 240% of P when you solve for profit. Plugging them into the relationships leads to contradictions. Only Rs 1,190 fits both the given selling price and the specified percentage relationship between cost price and profit.

Common Pitfalls:
Many students misread “240% more than the profit” as “240% of the profit” and set CP = 2.4P instead of 3.4P. Others mistakenly try to interpret 240% as a profit percentage on cost price. Always read such statements carefully, distinguishing between “is 240% of” and “is 240% more than,” as they mean different things mathematically.

Final Answer:
The cost price of the college bag is Rs. 1190.