Profit And Loss
Math MCQs

Question :    Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

Correct Answer  4710

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) = $16014

And, the profit = 240%

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 + 240} × 16014

= ^{100 × 16014}/₃₄₀

= ^1601400/₃₄₀ = 4710

Thus, the Cost Price (CP) = $4710 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 = 240%

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

= 240% of m

= 240% × m

= ²⁴⁰/₁₀₀ × m

⇒ Profit = ^{240 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 16014 = m + ^{240 m}/₁₀₀

⇒ 16014 = ^{100 m + 240 m}/₁₀₀

⇒ 16014 = ^{340 m}/₁₀₀

After cross multiplication, we get

16014 × 100 = 340 m

⇒ 340 m = 16014 × 100

⇒ m = ^{16014 × 100}/₃₄₀

⇒ m = ^1601400/₃₄₀ = 4710

⇒ m = 4710

Thus, the Cost Price (CP) = $4710 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) = $16014

And, the profit = 240%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 240% of 100 = 240

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

⇒ Sale Price (SP) = 100 + 240

⇒ Sale Price (SP) = 340

∵ If the Sale Price (SP) is 340, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₄₀

∴ If the Sale Price (SP) is 16014, then the Cost Price (CP)

= ¹⁰⁰/₃₄₀ × 16014

= ^{100 × 16014}/₃₄₀

= ^1601400/₃₄₀ = 4710

Thus, the Cost Price (CP) = $4710 Answer

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

Given, the sale price (SP) = $16014

And, the profit = 240%

Then, the Cost Price (CP) = ?

SP = 340% of CP

⇒ SP = ³⁴⁰/₁₀₀ × CP

⇒ 16014 = ^{340 CP}/₁₀₀

After cross multiplication

⇒ 16014 × 100 = 340 CP

⇒ 340 CP = 16014 × 100

⇒ CP = ^{16014 × 100}/₃₄₀

⇒ CP = ^1601400/₃₄₀ = 4710

⇒ CP = $4710 Answer

Similar Questions

(1) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.

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

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

(4) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

(5) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

(6) Find the cost price, if a share broker gets a loss of 26% by selling 100 shares for $3707.40.

(7) A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.

(8) A shopkeeper gets a loss of 5% by selling some fruits for $769.50. Find the cost price of the furits.

(9) If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

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