Shortcut Trick
Using the direct ratio relation: MP / CP = (100 − Loss%) / (100 − Discount%)
⇒ 72000 / CP = (100 − 10) / (100 − 20) = 90 / 80 = 9 / 8
⇒ Cost Price (CP) = 72000 × 8 ÷ 9 = &rupee;64000
⇒ Desired Selling Price to gain &rupee;440 = 64000 + 440 = &rupee;64440
⇒ Required Discount % = [(72000 − 64440) ÷ 72000] × 100 = (7560 ÷ 72000) × 100 = 10.5%
∴ The correct answer is 10.5%.
Alternate Method
Given:
Marked Price (MP) = &rupee;72000
Initial Discount = 20%
Initial Loss = 10%
Desired Gain = &rupee;440
Formula Used:
Selling Price (SP) = MP × (100 − Discount%) ÷ 100
Cost Price (CP) = SP × 100 ÷ (100 − Loss%)
Discount % = [(MP − SP) ÷ MP] × 100
Calculations:
⇒ Initial SP = 72000 × (100 − 20) ÷ 100 = 72000 × 0.8 = &rupee;57600
⇒ CP = 57600 × 100 ÷ (100 − 10) = 57600 × 100 ÷ 90 = &rupee;64000
⇒ New SP for a gain of &rupee;440 = CP + Gain = 64000 + 440 = &rupee;64440
⇒ New Discount = MP − New SP = 72000 − 64440 = &rupee;7560
⇒ Required Discount % = (7560 ÷ 72000) × 100 = 10.5%
CP = ₹64000
SP = ₹64440
MP = ₹72000
Discount % = (7560 / 72000) × 100 = 10.5%
∴ The correct answer is 10.5%.
Additional Information
Marked Price & Cost Price Relation
The direct ratio between Marked Price (MP) and Cost Price (CP) is computed as MP / CP = (100 ± Profit/Loss%) ÷ (100 − Discount%).
Successive Discounts
If two successive discounts of a% and b% are given, the equivalent single discount percentage is (a + b − a×b ÷ 100)%.
Dishonest Dealer Formula
When a dealer sells goods at cost price but uses a false weight, the actual Profit % = (True Weight − False Weight) ÷ False Weight × 100.