Profit And Loss
Math MCQs

Question :    Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

Correct Answer  6510

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) = $27993

And, the profit = 330%

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 + 330} × 27993

= ^{100 × 27993}/₄₃₀

= ^2799300/₄₃₀ = 6510

Thus, the Cost Price (CP) = $6510 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 = 330%

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

= 330% of m

= 330% × m

= ³³⁰/₁₀₀ × m

⇒ Profit = ^{330 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 27993 = m + ^{330 m}/₁₀₀

⇒ 27993 = ^{100 m + 330 m}/₁₀₀

⇒ 27993 = ^{430 m}/₁₀₀

After cross multiplication, we get

27993 × 100 = 430 m

⇒ 430 m = 27993 × 100

⇒ m = ^{27993 × 100}/₄₃₀

⇒ m = ^2799300/₄₃₀ = 6510

⇒ m = 6510

Thus, the Cost Price (CP) = $6510 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) = $27993

And, the profit = 330%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 330% of 100 = 330

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

⇒ Sale Price (SP) = 100 + 330

⇒ Sale Price (SP) = 430

∵ If the Sale Price (SP) is 430, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₃₀

∴ If the Sale Price (SP) is 27993, then the Cost Price (CP)

= ¹⁰⁰/₄₃₀ × 27993

= ^{100 × 27993}/₄₃₀

= ^2799300/₄₃₀ = 6510

Thus, the Cost Price (CP) = $6510 Answer

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

Given, the sale price (SP) = $27993

And, the profit = 330%

Then, the Cost Price (CP) = ?

SP = 430% of CP

⇒ SP = ⁴³⁰/₁₀₀ × CP

⇒ 27993 = ^{430 CP}/₁₀₀

After cross multiplication

⇒ 27993 × 100 = 430 CP

⇒ 430 CP = 27993 × 100

⇒ CP = ^{27993 × 100}/₄₃₀

⇒ CP = ^2799300/₄₃₀ = 6510

⇒ CP = $6510 Answer

Similar Questions

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

(2) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.

(3) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

(4) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(5) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

(6) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?

(7) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?

(8) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(9) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?

(10) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.