Profit And Loss
Math MCQs

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

Correct Answer  6710

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) = $29524

And, the profit = 340%

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 + 340} × 29524

= ^{100 × 29524}/₄₄₀

= ^2952400/₄₄₀ = 6710

Thus, the Cost Price (CP) = $6710 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 = 340%

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

= 340% of m

= 340% × m

= ³⁴⁰/₁₀₀ × m

⇒ Profit = ^{340 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 29524 = m + ^{340 m}/₁₀₀

⇒ 29524 = ^{100 m + 340 m}/₁₀₀

⇒ 29524 = ^{440 m}/₁₀₀

After cross multiplication, we get

29524 × 100 = 440 m

⇒ 440 m = 29524 × 100

⇒ m = ^{29524 × 100}/₄₄₀

⇒ m = ^2952400/₄₄₀ = 6710

⇒ m = 6710

Thus, the Cost Price (CP) = $6710 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) = $29524

And, the profit = 340%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 340% of 100 = 340

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

⇒ Sale Price (SP) = 100 + 340

⇒ Sale Price (SP) = 440

∵ If the Sale Price (SP) is 440, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₄₀

∴ If the Sale Price (SP) is 29524, then the Cost Price (CP)

= ¹⁰⁰/₄₄₀ × 29524

= ^{100 × 29524}/₄₄₀

= ^2952400/₄₄₀ = 6710

Thus, the Cost Price (CP) = $6710 Answer

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

Given, the sale price (SP) = $29524

And, the profit = 340%

Then, the Cost Price (CP) = ?

SP = 440% of CP

⇒ SP = ⁴⁴⁰/₁₀₀ × CP

⇒ 29524 = ^{440 CP}/₁₀₀

After cross multiplication

⇒ 29524 × 100 = 440 CP

⇒ 440 CP = 29524 × 100

⇒ CP = ^{29524 × 100}/₄₄₀

⇒ CP = ^2952400/₄₄₀ = 6710

⇒ CP = $6710 Answer

Similar Questions

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

(2) What will be profit percent if John buys 6 articles for $1 and sells 5 articles for $1?

(3) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

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

(5) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.

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

(7) A trader loses 48% by selling an article for $1175.20. For how much should he sell it to get a profit of 47%?

(8) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(9) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.

(10) Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?