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) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

(3) Mr. Oliver loses 82% by selling an article for $712.80. For how much should he sell it to get a profit of 81%?

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

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

(6) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.

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

(8) A trader gets a loss of 52% by selling 500 bags of rice for $4900.80. Find the cost price of rice.

(9) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

(10) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?