A shopkeeper sells cashew nuts at Rs 1260 per kilogram and incurs a loss of 8%. If he decides to sell at Rs 1386 per kilogram instead, what will be his new percentage gain or loss?

Introduction / Context:
This problem focuses on changing the selling price of a commodity and observing how the profit or loss percentage changes while the cost price remains fixed. Initially, cashew nuts are sold at a loss, but after increasing the selling price, the shopkeeper may move into a small profit. The question tests your ability to find cost price from a known loss situation and then recompute the new profit percentage with a different selling price.

Given Data / Assumptions:

• Initial selling price SP1 = Rs 1260 per kg.
• Initial transaction gives a loss of 8%.
• New selling price SP2 = Rs 1386 per kg.
• We need the new profit or loss percentage.
• The cost price per kg remains constant between the two situations.

Concept / Approach:
Use loss formula to find cost price:

• Loss 8% means SP1 = 0.92 * CP.
• From SP1, compute CP = SP1 / 0.92.
• Then compare SP2 with CP using profit or loss percentage = ((SP2 - CP) / CP) * 100.

This sequence shows how a change in selling price can flip loss into gain.

Step-by-Step Solution:
Step 1: Let cost price per kg = CP. Step 2: Loss of 8% means SP1 = 0.92 * CP. Step 3: We know SP1 = 1260, so 1260 = 0.92 * CP. Step 4: CP = 1260 / 0.92. Step 5: Compute using fraction form: 0.92 = 92 / 100, so CP = 1260 * 100 / 92 = 126000 / 92 = 31500 / 23. Step 6: New selling price SP2 = 1386. Step 7: Profit or loss fraction = (SP2 - CP) / CP = (1386 - CP) / CP. Step 8: Use CP = 31500 / 23. Then SP2 - CP = 1386 - 31500 / 23 = (1386 * 23 - 31500) / 23 = (31878 - 31500) / 23 = 378 / 23. Step 9: Profit fraction = (378 / 23) / (31500 / 23) = 378 / 31500 = 63 / 5250 = 1 / 83.333... Step 10: Profit percentage ≈ (1 / 83.333...) * 100 = 1.2% gain.

Verification / Alternative check:
Approximate CP numerically:

• CP ≈ 1260 / 0.92 ≈ Rs 1369.565.
• Difference between new SP and CP = 1386 - 1369.565 ≈ 16.435.
• Profit percentage ≈ 16.435 / 1369.565 * 100 ≈ 1.20%.

This confirms a small positive profit of around 1.2%, consistent with the exact fractional calculation, so the new selling price yields a modest gain.

Why Other Options Are Wrong:
2.4 percent gain: This would require the difference between SP2 and CP to be roughly double what we computed.
1.2 percent loss: Incorrect because SP2 is actually slightly higher than CP, not lower.
2.4 percent loss: Also impossible since a higher selling price than cost price cannot produce a loss.
Only 1.2 percent gain matches both exact and approximate calculations.

Common Pitfalls:
Some students invert the formula and compute CP as 0.92 * 1260, which is wrong because loss percentage is given on CP, not on SP. Others may accidentally treat 1260 as CP and directly compute profit with the new SP, ignoring that the initial situation involved a loss. Always reconstruct CP correctly from the given loss information before re-evaluating profit or loss at a new selling price.

Final Answer:
When the selling price is increased to Rs 1386 per kilogram, the shopkeeper makes a 1.2 percent gain on cashew nuts.