A shopkeeper sells dried apricots at Rs 1310 per kilogram and incurs a loss of 13%. If he raises the selling price to Rs 1441 per kilogram, what will be his new percentage gain or loss?

Introduction / Context:
This question is similar in structure to other profit and loss problems where a new selling price changes the magnitude of loss or profit. Initially, dried apricots are sold at a certain loss percent. After increasing the selling price, the shopkeeper still may have a loss, but usually a smaller one. The task is to compute the new percentage gain or loss after the price change, using the fact that cost price remains fixed.

Given Data / Assumptions:

• Initial selling price SP1 = Rs 1310 per kg.
• Initial loss = 13%.
• New selling price SP2 = Rs 1441 per kg.
• We must determine whether SP2 leads to profit or loss, and its percentage.
• Cost price per kg is constant between both scenarios.

Concept / Approach:
We again use the loss formula to find cost price:

• Loss 13% means SP1 = 0.87 * CP.
• Thus CP = SP1 / 0.87.
• Compare SP2 with CP using percentage formula: (SP2 - CP) / CP * 100.

A positive result gives profit; a negative result gives loss.

Step-by-Step Solution:
Step 1: Let cost price per kg = CP. Step 2: Loss of 13% implies SP1 = 0.87 * CP. Step 3: SP1 = 1310, so 1310 = 0.87 * CP. Step 4: CP = 1310 / 0.87. Step 5: Express 0.87 as 87 / 100, so CP = 1310 * 100 / 87 = 131000 / 87. Step 6: New selling price SP2 = 1441. Step 7: Profit or loss fraction = (SP2 - CP) / CP. Step 8: Compute SP2 - CP in fractional form: SP2 - CP = 1441 - 131000 / 87. Step 9: Convert 1441 to denominator 87: 1441 = 1441 * 87 / 87 = 125367 / 87. Step 10: Difference = (125367 - 131000) / 87 = -5633 / 87, which is negative, so it is a loss. Step 11: Loss fraction = (5633 / 87) / (131000 / 87) = 5633 / 131000 ≈ 0.043. Step 12: Loss percentage ≈ 0.043 * 100 = 4.3% loss.

Verification / Alternative check:
Approximate CP numerically:

• CP ≈ 1310 / 0.87 ≈ Rs 1505.75.
• Difference between CP and SP2 = 1505.75 - 1441 ≈ 64.75.
• Loss percentage ≈ 64.75 / 1505.75 * 100 ≈ 4.3%.

This confirms that even with the increased selling price, the shopkeeper still faces a small loss of about 4.3% per kilogram.

Why Other Options Are Wrong:
8.6 percent loss: This is larger than the computed loss and does not correspond to the new price.
4.3 percent gain: Incorrect because SP2 is still lower than CP, so a gain is impossible.
8.6 percent gain: Also impossible because a selling price below cost price can never create profit.
Only 4.3 percent loss matches both exact fractional and approximate numerical calculations.

Common Pitfalls:
One frequent error is taking 1310 as cost price and computing profit directly from 1441. This ignores the initial loss percentage and leads to incorrect conclusions. Another mistake is to treat the 13% loss as being on the selling price instead of on cost price. Always remember: loss percentage is defined relative to cost price unless otherwise stated. Correctly reconstructing CP from SP1 is the key step.

Final Answer:
At the new selling price of Rs 1441 per kilogram, the shopkeeper incurs a 4.3 percent loss on dried apricots.