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Examoogle • User • info@examoogle.com • EE-2024-8821
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An article is sold at a profit of 64%. If the cost price is increased by ₹60 and the selling price is reduced by ₹65, then the profit would be 42.5%. What is the original cost price (in ₹) of the article?
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Shortcut Trick Initial profit = 64% ⇒ SP1 = 1.64 × CP1 New profit = 42.5% on (CP1 + 60) ⇒ SP2 = 1.425 × (CP1 + 60) Given change in SP: SP1 − SP2 = 65 1.64 × CP1 − 1.425 × (CP1 + 60) = 65 0.215 × CP1 = 65 + 85.5 = 150.5 CP1 = 150.5 ÷ 0.215 = 700 ∴ ...
Shortcut Trick
Initial profit = 64% ⇒ SP₁ = 1.64 × CP₁
New profit = 42.5% on (CP₁ + 60) ⇒ SP₂ = 1.425 × (CP₁ + 60)
Given change in SP: SP₁ − SP₂ = 65
1.64 × CP₁ − 1.425 × (CP₁ + 60) = 65
0.215 × CP₁ = 65 + 85.5 = 150.5
CP₁ = 150.5 ÷ 0.215 = 700
∴ The correct answer is ₹700.
Alternate Method
Given:
Initial Profit% = 64%
New Profit% = 42.5%
Increase in Cost Price (CP) = ₹60
Decrease in Selling Price (SP) = ₹65
Formula Used:
SP = CP × (1 + Profit/100)
Let the original cost price be x.
⇒ Original Selling Price = x + 0.64x = 1.64x
⇒ New Cost Price = x + 60
⇒ New Selling Price = 1.64x − 65
According to the problem, New SP = New CP × (100 + 42.5)/100
⇒ 1.64x − 65 = (x + 60) × 1.425
⇒ 1.64x − 65 = 1.425x + (60 × 1.425)
⇒ 1.64x − 65 = 1.425x + 85.5
⇒ 1.64x − 1.425x = 85.5 + 65
⇒ 0.215x = 150.5
⇒ x = 150.5 ÷ 0.215
⇒ x = 150500 ÷ 215
⇒ x = 700
∴ The correct answer is ₹700.
Additional Information
Profit and Loss Basics
Profit = SP − CP. Profit Percentage = (Profit ÷ CP) × 100.
Effect of Changes on CP and SP
If CP increases and SP decreases, the profit percentage always reduces. The relationship is governed by: New SP = New CP × (100 + New Profit%)/100.
Markup and Discount
Marked Price (MP) = CP + Markup. SP = MP − Discount. Profit can also be calculated as: Profit% = Markup% − Discount% − (Markup% × Discount% ÷ 100).