Shortcut Trick
When Selling Price (SP) is same for two articles with gain x% and loss y%:
Overall % = [100(x − y) − 2xy] ÷ [200 + x − y]
Given: x = 15, y = 13
Overall % = [100(15 − 13) − 2(15)(13)] ÷ [200 + 15 − 13] = [200 − 390] ÷ 202 = −190 ÷ 202 ≈ −0.94%
∴ The correct answer is 0.94% loss.
Alternate Method
Given: Selling Price of each article = ₹10,005 | Gain on 1st = 15% | Loss on 2nd = 13%
Formula: Cost Price (CP) = [SP ÷ (100 ± Profit/Loss%)] × 100
⇒ CP of Article 1 = 10,005 ÷ 1.15 = ₹8,700
⇒ CP of Article 2 = 10,005 ÷ 0.87 = ₹11,500
⇒ Total CP = 8,700 + 11,500 = ₹20,200
⇒ Total SP = 10,005 + 10,005 = ₹20,010
⇒ Overall Loss = 20,200 − 20,010 = ₹190
⇒ Loss % = (190 ÷ 20,200) × 100 = 190 ÷ 202 ≈ 0.9405%
∴ The correct answer is 0.94% loss.
Additional Information
Standard Equal Profit/Loss Case
If SP is same and there is x% gain and x% loss, there is always a net loss of x2 ÷ 100%.
Successive Percentage Formula
For two successive changes a% and b%, the effective change is [a + b + (ab/100)]% (not directly applicable here as base CP is different).
Ratio Method
Convert percentage to fractions (15% = 3/20, 13% = 13/100) and equate the SP units to find the combined CP and SP ratio.