Profit And Loss
Math MCQs

Question :    By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

Correct Answer  5510

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) = $20938

And, the profit = 280%

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 + 280} × 20938

= ^{100 × 20938}/₃₈₀

= ^2093800/₃₈₀ = 5510

Thus, the Cost Price (CP) = $5510 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 = 280%

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

= 280% of m

= 280% × m

= ²⁸⁰/₁₀₀ × m

⇒ Profit = ^{280 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 20938 = m + ^{280 m}/₁₀₀

⇒ 20938 = ^{100 m + 280 m}/₁₀₀

⇒ 20938 = ^{380 m}/₁₀₀

After cross multiplication, we get

20938 × 100 = 380 m

⇒ 380 m = 20938 × 100

⇒ m = ^{20938 × 100}/₃₈₀

⇒ m = ^2093800/₃₈₀ = 5510

⇒ m = 5510

Thus, the Cost Price (CP) = $5510 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) = $20938

And, the profit = 280%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 280% of 100 = 280

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

⇒ Sale Price (SP) = 100 + 280

⇒ Sale Price (SP) = 380

∵ If the Sale Price (SP) is 380, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₈₀

∴ If the Sale Price (SP) is 20938, then the Cost Price (CP)

= ¹⁰⁰/₃₈₀ × 20938

= ^{100 × 20938}/₃₈₀

= ^2093800/₃₈₀ = 5510

Thus, the Cost Price (CP) = $5510 Answer

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

Given, the sale price (SP) = $20938

And, the profit = 280%

Then, the Cost Price (CP) = ?

SP = 380% of CP

⇒ SP = ³⁸⁰/₁₀₀ × CP

⇒ 20938 = ^{380 CP}/₁₀₀

After cross multiplication

⇒ 20938 × 100 = 380 CP

⇒ 380 CP = 20938 × 100

⇒ CP = ^{20938 × 100}/₃₈₀

⇒ CP = ^2093800/₃₈₀ = 5510

⇒ CP = $5510 Answer

Similar Questions

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

(2) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

(3) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

(4) If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

(5) Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5

(6) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

(7) Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.

(8) If a trader earns a profit of 10% by selling rice for $121 per kg, then find the cost price of the rice

(9) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(10) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00