Profit And Loss
Math MCQs

Question :    A trader earns a profit of 205% by selling some articles for $12230.50. What was the cost price?

Correct Answer  4010

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) = $12230.5

And, the profit = 205%

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 + 205} × 12230.5

= ^{100 × 12230.5}/₃₀₅

= ^1223050/₃₀₅ = 4010

Thus, the Cost Price (CP) = $4010 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 = 205%

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

= 205% of m

= 205% × m

= ²⁰⁵/₁₀₀ × m

⇒ Profit = ^{205 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 12230.5 = m + ^{205 m}/₁₀₀

⇒ 12230.5 = ^{100 m + 205 m}/₁₀₀

⇒ 12230.5 = ^{305 m}/₁₀₀

After cross multiplication, we get

12230.5 × 100 = 305 m

⇒ 305 m = 12230.5 × 100

⇒ m = ^{12230.5 × 100}/₃₀₅

⇒ m = ^1223050/₃₀₅ = 4010

⇒ m = 4010

Thus, the Cost Price (CP) = $4010 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) = $12230.5

And, the profit = 205%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 205% of 100 = 205

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

⇒ Sale Price (SP) = 100 + 205

⇒ Sale Price (SP) = 305

∵ If the Sale Price (SP) is 305, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₀₅

∴ If the Sale Price (SP) is 12230.5, then the Cost Price (CP)

= ¹⁰⁰/₃₀₅ × 12230.5

= ^{100 × 12230.5}/₃₀₅

= ^1223050/₃₀₅ = 4010

Thus, the Cost Price (CP) = $4010 Answer

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

Given, the sale price (SP) = $12230.5

And, the profit = 205%

Then, the Cost Price (CP) = ?

SP = 305% of CP

⇒ SP = ³⁰⁵/₁₀₀ × CP

⇒ 12230.5 = ^{305 CP}/₁₀₀

After cross multiplication

⇒ 12230.5 × 100 = 305 CP

⇒ 305 CP = 12230.5 × 100

⇒ CP = ^{12230.5 × 100}/₃₀₅

⇒ CP = ^1223050/₃₀₅ = 4010

⇒ CP = $4010 Answer

Similar Questions

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(2) John sold rice at $7.20 per kg. If he purchased 120 kg of rice for $960, then calculate the loss and loss percent in this sale.

(3) Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.

(4) A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?

(5) Find the cost price, if a broker earns a profit of 370% by selling an old house for $34357

(6) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

(7) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(8) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(9) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

(10) If a peddler bought 71 paper clips for $1 and sold 70 paper clips for $1 then, find the profit in percent.