Profit And Loss
Math MCQs

Question :    Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

Correct Answer  4510

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) = $14883

And, the profit = 230%

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 + 230} × 14883

= ^{100 × 14883}/₃₃₀

= ^1488300/₃₃₀ = 4510

Thus, the Cost Price (CP) = $4510 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 = 230%

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

= 230% of m

= 230% × m

= ²³⁰/₁₀₀ × m

⇒ Profit = ^{230 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 14883 = m + ^{230 m}/₁₀₀

⇒ 14883 = ^{100 m + 230 m}/₁₀₀

⇒ 14883 = ^{330 m}/₁₀₀

After cross multiplication, we get

14883 × 100 = 330 m

⇒ 330 m = 14883 × 100

⇒ m = ^{14883 × 100}/₃₃₀

⇒ m = ^1488300/₃₃₀ = 4510

⇒ m = 4510

Thus, the Cost Price (CP) = $4510 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) = $14883

And, the profit = 230%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 230% of 100 = 230

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

⇒ Sale Price (SP) = 100 + 230

⇒ Sale Price (SP) = 330

∵ If the Sale Price (SP) is 330, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₃₀

∴ If the Sale Price (SP) is 14883, then the Cost Price (CP)

= ¹⁰⁰/₃₃₀ × 14883

= ^{100 × 14883}/₃₃₀

= ^1488300/₃₃₀ = 4510

Thus, the Cost Price (CP) = $4510 Answer

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

Given, the sale price (SP) = $14883

And, the profit = 230%

Then, the Cost Price (CP) = ?

SP = 330% of CP

⇒ SP = ³³⁰/₁₀₀ × CP

⇒ 14883 = ^{330 CP}/₁₀₀

After cross multiplication

⇒ 14883 × 100 = 330 CP

⇒ 330 CP = 14883 × 100

⇒ CP = ^{14883 × 100}/₃₃₀

⇒ CP = ^1488300/₃₃₀ = 4510

⇒ CP = $4510 Answer

Similar Questions

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(3) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

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(5) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

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(8) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

(9) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

(10) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.