Shortcut Trick
When two items are sold at the same price with an equal percentage of profit and loss (x%), the transaction always results in an overall loss.
Overall Loss % = (x2 ÷ 100) %
Here, the profit and loss percentages are equal, so x = 22.
Overall Loss % = (222 ÷ 100) % = (484 ÷ 100) % = 4.84%
∴ The correct answer is 4.84% loss.
Alternate Method
Given:
Profit on Dog 1 = 22%
Loss on Dog 2 = 22%
Selling Price of Dog 1 = Selling Price of Dog 2
Formula Used:
Cost Price (CP) = [100 ÷ (100 + Profit %)] × SP
Cost Price (CP) = [100 ÷ (100 − Loss %)] × SP
Loss % = (Total Loss ÷ Total CP) × 100
Dog 1 (CP&sub1;)
Dog 2 (CP&sub2;)
Same SP
Calculations:
Let the Selling Price (SP) of each dog be 100 units.
⇒ Total SP = 100 + 100 = 200 units
⇒ CP of Dog 1 (sold at 22% profit) = (100 ÷ 122) × 100 = 10000 ÷ 122 = 5000 ÷ 61 units
⇒ CP of Dog 2 (sold at 22% loss) = (100 ÷ 78) × 100 = 10000 ÷ 78 = 5000 ÷ 39 units
⇒ Total CP = (5000 ÷ 61) + (5000 ÷ 39)
⇒ Total CP = 5000 × [(39 + 61) ÷ (61 × 39)]
⇒ Total CP = 5000 × [100 ÷ 2379] = 500000 ÷ 2379 units
⇒ Total Loss = Total CP − Total SP
⇒ Total Loss = (500000 ÷ 2379) − 200
⇒ Total Loss = (500000 − 475800) ÷ 2379 = 24200 ÷ 2379 units
⇒ Loss % = (Total Loss ÷ Total CP) × 100
⇒ Loss % = [(24200 ÷ 2379) ÷ (500000 ÷ 2379)] × 100
⇒ Loss % = (24200 ÷ 500000) × 100
⇒ Loss % = 242 ÷ 50 = 4.84%
∴ The correct answer is 4.84% loss.
Additional Information
Case of Same Cost Price (CP)
If two articles are bought at the same price and one is sold at x% profit and the other at x% loss, then there is strictly NO profit and NO loss overall.
Successive Discounts
When two consecutive discounts of a% and b% are applied on an item, the effective single equivalent discount is (a + b − ab ÷ 100)%.
Dishonest Dealer Formula
If a seller claims to sell goods at Cost Price but uses a faulty weight, the Profit % = [(True Weight − False Weight) ÷ False Weight] × 100.