Shortcut Trick
Price ratio (CP : SP) = 20 : 30 = 2 : 3
Weight ratio (Actual : Claimed) = 800 : 1000 = 4 : 5
Effective CP : SP ratio = (2 × 4) : (3 × 5) = 8 : 15
Profit = 15 − 8 = 7 units.
Profit % = (7 ÷ 8) × 100 = 87.5%
∴ The correct answer is 87.5%.
Alternate Method
Given:
Cost price of 1 kg (1000 g) mangoes = Rs. 20
Selling price of 1 kg mangoes = Rs. 30
Actual weight given instead of 1 kg = 800 g
Calculations:
⇒ Cost price of 1 g mango = 20 ÷ 1000 = Rs. 0.02
⇒ Actual cost price of 800 g mangoes = 800 × 0.02 = Rs. 16
⇒ The shopkeeper charges Rs. 30 for 800 g (claiming it as 1 kg).
⇒ Actual Selling price = Rs. 30
⇒ Profit = SP − Actual CP
⇒ Profit = 30 − 16 = Rs. 14
⇒ Profit % = (Profit ÷ Actual CP) × 100
⇒ Profit % = (14 ÷ 16) × 100 = 87.5%
∴ The correct answer is 87.5%.
Additional Information
Dishonest Dealer Concept
When a dealer sells goods using false weights, the actual cost price is based on the true weight delivered to the customer, while the selling price is based on the claimed weight.
Successive Ratio Method
The overall profit ratio can be derived by multiplying the individual price markup ratio (CP : SP) by the cheating weight ratio (Actual Weight : Claimed Weight).
Profit % Formula
Profit % = [(SP − Actual CP) ÷ Actual CP] × 100