Shortcut Trick
Ratio of Marked Price (MP) to Cost Price (CP) = (100 + Profit%) : (100 − Discount%)
Ratio MP : CP = (100 + 15) : (100 − 20) = 115 : 80 = 23 : 16
Given, CP = 16 units = ₹5,600 ⇒ 1 unit = ₹350
MP = 23 units = 23 × 350 = ₹8,050
∴ The correct answer is ₹8,050.
Alternate Method
Given: Cost Price (CP) = ₹5,600, Profit = 15%, Discount = 20%.
Formula Used: Selling Price (SP) = CP × (1 + Profit/100) and Marked Price (MP) = SP / (1 − Discount/100).
⇒ Selling Price (SP) = 5600 + (15% of 5600)
⇒ SP = 5600 + (15/100 × 5600) = 5600 + 840 = ₹6,440
⇒ Let Marked Price (MP) be M.
⇒ SP = M − (20% of M) = 80% of M
⇒ 6440 = (80/100) × M
⇒ M = (6440 × 100) / 80 = 6440 / 0.8
⇒ M = ₹8,050
Therefore, Option (4) is the correct choice as it matches the calculated Marked Price.
∴ The correct answer is ₹8,050.
Additional Information
Relation between CP and MP
The direct formula is MP/CP = (100 + P%)/(100 − D%). This helps find the markup or CP/MP quickly when both profit and discount percentages are known.
Successive Discount
If two discounts d1 and d2 are given, the equivalent single discount is (d1 + d2 − (d1 × d2)/100)%.
Markup Percentage
Markup % = ((MP − CP) / CP) × 100. It represents how much the price is increased over the cost price before offering a discount.