Profit And Loss
Math MCQs

Question :    In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

Correct Answer  6410

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) = $27242.5

And, the profit = 325%

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 + 325} × 27242.5

= ^{100 × 27242.5}/₄₂₅

= ^2724250/₄₂₅ = 6410

Thus, the Cost Price (CP) = $6410 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 = 325%

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

= 325% of m

= 325% × m

= ³²⁵/₁₀₀ × m

⇒ Profit = ^{325 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 27242.5 = m + ^{325 m}/₁₀₀

⇒ 27242.5 = ^{100 m + 325 m}/₁₀₀

⇒ 27242.5 = ^{425 m}/₁₀₀

After cross multiplication, we get

27242.5 × 100 = 425 m

⇒ 425 m = 27242.5 × 100

⇒ m = ^{27242.5 × 100}/₄₂₅

⇒ m = ^2724250/₄₂₅ = 6410

⇒ m = 6410

Thus, the Cost Price (CP) = $6410 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) = $27242.5

And, the profit = 325%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 325% of 100 = 325

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

⇒ Sale Price (SP) = 100 + 325

⇒ Sale Price (SP) = 425

∵ If the Sale Price (SP) is 425, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₂₅

∴ If the Sale Price (SP) is 27242.5, then the Cost Price (CP)

= ¹⁰⁰/₄₂₅ × 27242.5

= ^{100 × 27242.5}/₄₂₅

= ^2724250/₄₂₅ = 6410

Thus, the Cost Price (CP) = $6410 Answer

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

Given, the sale price (SP) = $27242.5

And, the profit = 325%

Then, the Cost Price (CP) = ?

SP = 425% of CP

⇒ SP = ⁴²⁵/₁₀₀ × CP

⇒ 27242.5 = ^{425 CP}/₁₀₀

After cross multiplication

⇒ 27242.5 × 100 = 425 CP

⇒ 425 CP = 27242.5 × 100

⇒ CP = ^{27242.5 × 100}/₄₂₅

⇒ CP = ^2724250/₄₂₅ = 6410

⇒ CP = $6410 Answer

Similar Questions

(1) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

(2) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(3) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(4) Mr. Joseph loses 5% by selling an article for $104.50. For how much should he sell it to get a profit of 4%?

(5) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(6) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

(7) Calculate the earnings percentage if a hawker buys 58 articles for $1 and sells 57 articles for $1.

(8) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

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

(10) Find the cost price, if a trader gets a loss of 57% by selling a TV set for $4820.30