Shortcut Trick
Ratio of Initial MP to CP = (100 + Profit%) ÷ (100 − Discount%) = 105 ÷ 90 = 7/6
New MP = Initial MP × 1.05 = (7/6) × 1.05 = 1.225 times of CP
Multiplier for two 5% successive discounts = 0.95 × 0.95 = 0.9025
Ratio of New SP to CP = 1.225 × 0.9025 = 1.10556
New Profit % = (1.10556 − 1) × 100 = 10.556% ≈ 10.5%
∴ The correct answer is 10.5%.
Alternate Method
Given:
⇒ Initial Discount (D) = 10%
⇒ Initial Profit (P) = 5%
⇒ Increase in Marked Price = 5%
⇒ Successive discounts on new MP = 5% and 5%
Formula Used:
⇒ MP = CP × (100 + P) ÷ (100 − D)
⇒ Equivalent Discount = d1 + d2 − (d1 × d2) ÷ 100
CP = 100MP₁ = 116.67+ 5%MP₂ = 122.5- 9.75%SP₂ = 110.56Profit = + 10.56%Markup
Calculations:
⇒ Let Cost Price (CP) = 100
⇒ Initial Selling Price (SP) = 100 + 5% of 100 = 105
⇒ Initial Marked Price (MP) = 105 ÷ (1 − 0.10) = 105 ÷ 0.90 = 116.67
⇒ New Marked Price = 116.67 × (1 + 0.05) = 116.67 × 1.05 = 122.5
⇒ Equivalent discount for two 5% discounts = 5 + 5 − (5 × 5) ÷ 100 = 10 − 0.25 = 9.75%
⇒ New Selling Price = 122.5 × (1 − 0.0975) = 122.5 × 0.9025 = 110.556
⇒ Overall Profit = New SP − CP = 110.556 − 100 = 10.556
⇒ Profit % = 10.556% ≈ 10.5%
∴ The correct answer is 10.5%.
Additional Information
Markup and Discount Relation
MP/CP = (100 + Profit%) ÷ (100 − Discount%). This direct ratio equation is highly useful for directly jumping between Marked Price and Cost Price without calculating the intermediate Selling Price.
Successive Discounts
Two successive discounts of x% and y% are structurally equivalent to a single effective discount of (x + y − xy÷100)%.
Base of Calculations
Unless specified otherwise, Profit and Loss are always evaluated on the Cost Price (CP), whereas Discounts are strictly evaluated on the Marked Price (MP).