Shortcut Trick
Total Selling Price (SP) = 15,000 × 2 = ₹30,000.
Total Cost Price (CP) = Total SP + Net Loss = 30,000 + 2000 = ₹32,000.
CP of 1st watch (sold at 25% profit) = 15,000 × (100 ÷ 125) = ₹12,000.
CP of 2nd watch = 32,000 − 12,000 = ₹20,000.
Loss% on 2nd watch = [(20,000 − 15,000) ÷ 20,000] × 100 = 25%.
∴ The correct answer is 25%.
Alternate Method
Given:
Selling price of each watch = ₹15,000
Profit on 1st watch = 25%
Net overall loss = ₹2000
Loss on 2nd watch = x%
Formula Used:
Cost Price (CP) = (SP × 100) ÷ (100 + Profit%)
Loss% = (Loss ÷ CP) × 100
CP = 12000
SP = 15000
Watch 1: +25% Profit
CP = 20000
SP = 15000
Watch 2: Loss = x%
Total CP = 32000
Total SP = 30000
Net Loss = 2000
Calculations:
⇒ Total SP of both watches = 15,000 + 15,000 = ₹30,000
⇒ Total CP = Total SP + Net loss
⇒ Total CP = 30,000 + 2000 = ₹32,000
⇒ CP of 1st watch = (15,000 × 100) ÷ (100 + 25)
⇒ CP of 1st watch = 1,500,000 ÷ 125 = ₹12,000
⇒ CP of 2nd watch = Total CP − CP of 1st watch
⇒ CP of 2nd watch = 32,000 − 12,000 = ₹20,000
⇒ Loss on 2nd watch = CP of 2nd watch − SP of 2nd watch
⇒ Loss on 2nd watch = 20,000 − 15,000 = ₹5,000
⇒ Loss% (x) = (5,000 ÷ 20,000) × 100
⇒ x = 25%
∴ The correct answer is 25%.
Additional Information
Marked Price and Discount
Discount is always calculated on Marked Price (MP), while Profit or Loss is calculated on Cost Price (CP). The relation is given by: SP = MP × (100 − Discount%) ÷ 100.
Successive Discounts
When two successive changes of a% and b% are applied on a base value, the net percentage change is given by the effective formula: Net Change = a + b + (a × b) ÷ 100.
Same Selling Price Concept
If two different items are sold at the same Selling Price, one at a profit of P% and the other at a loss of P%, there is always an overall net loss in the transaction which is given by: (P2 ÷ 100)%.