Shortcut Trick
Article 1: 50% Gain = 1/2 → CP1 : SP1 = 2 : 3.
Since Selling Price is same for both, let SP1 = SP2 = 3 units.
Total SP = 3 + 3 = 6 units. Given no Profit/Loss, Total CP must be 6 units.
CP2 = Total CP − CP1 = 6 − 2 = 4 units.
Article 2: CP = 4, SP = 3 ⇒ Loss = 1 unit on 4 units.
Loss % = (1 / 4) × 100 = 25%.
∴ The correct answer is 25%.
Alternate Method
Given:
Selling Price (SP) of each article = ₹2,178
Total Profit or Loss = 0 (No profit, no loss)
Profit % on Article 1 = 50%
Formula Used:
Cost Price (CP) = SP ÷ (1 + Gain%/100)
Loss % = (CP − SP) ÷ CP × 100
Calculations:
⇒ Total Selling Price = 2 × 2178 = ₹4,356
⇒ Since there is no Profit/Loss, Total Cost Price = ₹4,356
⇒ CP of Article 1 = 2178 ÷ (1 + 50/100) = 2178 ÷ 1.5
⇒ CP of Article 1 = 2178 × (2/3) = ₹1,452
⇒ CP of Article 2 = Total CP − CP of Article 1
⇒ CP of Article 2 = 4356 − 1452 = ₹2,904
⇒ Loss on Article 2 = CP2 − SP2 = 2904 − 2178 = ₹726
⇒ Loss % = (726 ÷ 2904) × 100
⇒ Loss % = (1 / 4) × 100 = 25%
∴ The correct answer is 25%.
Additional Information
Direct Formula for No Profit No Loss
When SP of two articles is same and overall Profit/Loss is zero, if one is sold at x% Profit, the other is sold at a Loss of: Loss% = (100 × x) ÷ (100 + 2x).
Case of Constant SP and Equal Profit/Loss%
If two articles are sold at the same SP, one at x% Profit and another at x% Loss, there is always an overall Loss of (x/10)2 %.
Relation between CP and SP
SP = CP × (100 + Profit%) ÷ 100 or SP = CP × (100 − Loss%) ÷ 100.