Shortcut Trick
Ratio of Profit : Loss = 29 : 1.
Total ratio parts = 29 + 1 = 30 units.
Difference between Selling Prices = 1200 − 600 = ₹600.
30 units = 600 ⇒ 1 unit (Loss) = ₹20.
Cost Price (CP) = 600 + 20 = ₹620.
Profit % = (Profit ÷ CP) × 100 = (580 ÷ 620) × 100 = 93.55%.
∴ The correct answer is 93.55 percent.
Alternate Method
Given:
Selling Price 1 (SP1) = ₹1200 (at Profit)
Selling Price 2 (SP2) = ₹600 (at Loss)
Profit = 29 × Loss
Formula Used:
Profit = Selling Price (SP) − Cost Price (CP)
Loss = Cost Price (CP) − Selling Price (SP)
Profit % = (Profit ÷ Cost Price) × 100
Calculations:
⇒ Let the Cost Price of the article be CP.
⇒ According to the question, Profit = 29 × Loss
⇒ (1200 − CP) = 29 × (CP − 600)
⇒ 1200 − CP = 29CP − 17400
⇒ 29CP + CP = 1200 + 17400
⇒ 30CP = 18600
⇒ CP = 18600 ÷ 30 = ₹620
⇒ Profit at SP ₹1200 = 1200 − 620 = ₹580
⇒ Profit % = (580 ÷ 620) × 100
⇒ Profit % = (29 ÷ 31) × 100 = 93.548...
⇒ Profit % ≈ 93.55%
∴ The correct answer is 93.55 percent.
Additional Information
Profit and Loss Percentage
Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price (CP) unless stated otherwise.
Selling Price Formula
When profit % is given: SP = CP × (100 + P%) ÷ 100. When loss % is given: SP = CP × (100 − L%) ÷ 100.
Successive Percentage Change
If there are two successive changes of a% and b%, the effective change is (a + b + ab/100)%.
∴ The correct answer is 93.55 percent.