Profit And Loss
Math MCQs

Question :    Find the cost price, if a dealer earns a profit of 305% by selling a plot for $24340.50

Correct Answer  6010

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) = $24340.5

And, the profit = 305%

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 + 305} × 24340.5

= ^{100 × 24340.5}/₄₀₅

= ^2434050/₄₀₅ = 6010

Thus, the Cost Price (CP) = $6010 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 = 305%

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

= 305% of m

= 305% × m

= ³⁰⁵/₁₀₀ × m

⇒ Profit = ^{305 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 24340.5 = m + ^{305 m}/₁₀₀

⇒ 24340.5 = ^{100 m + 305 m}/₁₀₀

⇒ 24340.5 = ^{405 m}/₁₀₀

After cross multiplication, we get

24340.5 × 100 = 405 m

⇒ 405 m = 24340.5 × 100

⇒ m = ^{24340.5 × 100}/₄₀₅

⇒ m = ^2434050/₄₀₅ = 6010

⇒ m = 6010

Thus, the Cost Price (CP) = $6010 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) = $24340.5

And, the profit = 305%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 305% of 100 = 305

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

⇒ Sale Price (SP) = 100 + 305

⇒ Sale Price (SP) = 405

∵ If the Sale Price (SP) is 405, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₀₅

∴ If the Sale Price (SP) is 24340.5, then the Cost Price (CP)

= ¹⁰⁰/₄₀₅ × 24340.5

= ^{100 × 24340.5}/₄₀₅

= ^2434050/₄₀₅ = 6010

Thus, the Cost Price (CP) = $6010 Answer

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

Given, the sale price (SP) = $24340.5

And, the profit = 305%

Then, the Cost Price (CP) = ?

SP = 405% of CP

⇒ SP = ⁴⁰⁵/₁₀₀ × CP

⇒ 24340.5 = ^{405 CP}/₁₀₀

After cross multiplication

⇒ 24340.5 × 100 = 405 CP

⇒ 405 CP = 24340.5 × 100

⇒ CP = ^{24340.5 × 100}/₄₀₅

⇒ CP = ^2434050/₄₀₅ = 6010

⇒ CP = $6010 Answer

Similar Questions

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(2) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(3) A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?

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(5) What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50

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(7) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.

(8) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(9) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?

(10) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.