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) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(2) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(3) Mrs. Julie buys 16 oranges for $1 and sells 15 oranges for $1. What is her profit percent in this sale?

(4) What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?

(5) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

(6) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(7) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

(8) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

(9) Mr. Steven loses 94% by selling an article for $273.60. For how much should he sell it to get a profit of 93%?

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