A shopkeeper sells cocoa seeds at Rs 1330 per kg and incurs a loss of 15%. If he instead sells them at Rs 1463 per kg, what is his percentage profit or loss?

Introduction / Context:
This question first gives a selling price at which the seller incurs a certain percentage loss and then changes the selling price. We are asked to determine the new profit or loss percentage at the new selling price. It is a good test of your ability to compute cost price from a given loss percentage and selling price, and then recompute profit or loss at a different selling price.

Given Data / Assumptions:

• At a selling price of Rs 1330 per kg, the shopkeeper has a loss of 15%.
• Later he sells at Rs 1463 per kg.
• We assume the cost price per kg of cocoa seeds is constant.
• We need to find the new profit or loss percentage at Rs 1463 per kg.

Concept / Approach:
When there is a loss of 15%, selling price SP1 = 85% of cost price CP:

• SP1 = 0.85 * CP.
• Given SP1 = 1330, so CP can be obtained.
• Once CP is known, compute new profit or loss using SP2 = 1463.
• New profit or loss percentage = ((SP2 - CP) / CP) * 100.

Step-by-Step Solution:
Let cost price per kg be CP. Given: at SP1 = 1330, loss is 15%. Therefore SP1 = 0.85 * CP. So 0.85 * CP = 1330. CP = 1330 / 0.85. CP ≈ 1564.71 (rounded to two decimal places). Now selling price SP2 = 1463. Profit or loss per kg = SP2 - CP ≈ 1463 - 1564.71 = -101.71. The negative sign indicates a loss of about Rs 101.71 per kg. Loss percentage ≈ (101.71 / 1564.71) * 100 ≈ 6.5%. Thus, at Rs 1463 per kg, he still incurs about 6.5% loss.

Verification / Alternative check:
We can approximate CP for quick checking. If CP were exactly 1565, then 15% of 1565 is about 234.75, and SP1 would be about 1330.25, close to 1330 after rounding. At SP2 = 1463, the difference from CP of about 1565 is around 102, which is roughly 6.5% of 1565. This supports our more exact calculation that the new loss percent is about 6.5%.

Why Other Options Are Wrong:
13% loss would mean the new selling price is even closer to the original loss case, which is not correct given the higher price. 6.5% gain would require SP2 to be above CP, but it is below CP. Likewise, 13% gain contradicts the loss situation. A 5% loss would require a selling price slightly closer to CP than 1463, so this option is also inaccurate. The correct approximate value is a 6.5% loss.

Common Pitfalls:
A common mistake is to assume that increasing the selling price from 1330 to 1463 automatically creates a profit, without first calculating the true cost price. Another error is to treat 15% as a fraction of the selling price rather than cost price. Always derive cost price accurately from the first scenario, then recompute any new profit or loss with respect to that same cost price.

Final Answer:
At the selling price of Rs 1463 per kg, the shopkeeper incurs approximately a 6.5% loss.