Profit And Loss
Math MCQs

Question :    Find the cost price, if Mrs. Olivia earns a profit of 160% by selling some articles for $8086

Correct Answer  3110

Solution & Explanation

Solution

Finding the cost price if the sale price and profit percent are known

The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.

Finding the cost price using the formula when the sale price and profit percent are known

Given, the sale price (SP) = $8086

And, the profit = 160%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and profit percent are known

Cost Price (CP) = ¹⁰⁰/_{100 + gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 + 160} × 8086

= ^{100 × 8086}/₂₆₀

= ⁸⁰⁸⁶⁰⁰/₂₆₀ = 3110

Thus, the Cost Price (CP) = $3110 Answer

Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given

Let the Cost Price (CP) = m

Here given profit = 160%

Calculation of Profit

Profit is calculated on cost price (CP)

Formula to find the Profit = Profit% of CP

Thus, profit on the cost price of m

= 160% of m

= 160% × m

= ¹⁶⁰/₁₀₀ × m

⇒ Profit = ^{160 m}/₁₀₀

Calculation of Cost Price (CP)

The Sale Price (SP) = Cost Price (CP) + Profit

⇒ 8086 = m + ^{160 m}/₁₀₀

⇒ 8086 = ^{100 m + 160 m}/₁₀₀

⇒ 8086 = ^{260 m}/₁₀₀

After cross multiplication, we get

8086 × 100 = 260 m

⇒ 260 m = 8086 × 100

⇒ m = ^{8086 × 100}/₂₆₀

⇒ m = ⁸⁰⁸⁶⁰⁰/₂₆₀ = 3110

⇒ m = 3110

Thus, the Cost Price (CP) = $3110 Answer

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given

Given, the sale price (SP) = $8086

And, the profit = 160%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 160% of 100 = 160

Thus, Sale Price (SP) = Cost Price (CP) + Profit

⇒ Sale Price (SP) = 100 + 160

⇒ Sale Price (SP) = 260

∵ If the Sale Price (SP) is 260, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₂₆₀

∴ If the Sale Price (SP) is 8086, then the Cost Price (CP)

= ¹⁰⁰/₂₆₀ × 8086

= ^{100 × 8086}/₂₆₀

= ⁸⁰⁸⁶⁰⁰/₂₆₀ = 3110

Thus, the Cost Price (CP) = $3110 Answer

Shortcut Method to find Cost Price (CP) when SP and profit percent are known

Given, the sale price (SP) = $8086

And, the profit = 160%

Then, the Cost Price (CP) = ?

SP = 260% of CP

⇒ SP = ²⁶⁰/₁₀₀ × CP

⇒ 8086 = ^{260 CP}/₁₀₀

After cross multiplication

⇒ 8086 × 100 = 260 CP

⇒ 260 CP = 8086 × 100

⇒ CP = ^{8086 × 100}/₂₆₀

⇒ CP = ⁸⁰⁸⁶⁰⁰/₂₆₀ = 3110

⇒ CP = $3110 Answer

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