Profit And Loss
Math MCQs

Question :    Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

Correct Answer  4510

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) = $14883

And, the profit = 230%

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 + 230} × 14883

= ^{100 × 14883}/₃₃₀

= ^1488300/₃₃₀ = 4510

Thus, the Cost Price (CP) = $4510 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 = 230%

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

= 230% of m

= 230% × m

= ²³⁰/₁₀₀ × m

⇒ Profit = ^{230 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 14883 = m + ^{230 m}/₁₀₀

⇒ 14883 = ^{100 m + 230 m}/₁₀₀

⇒ 14883 = ^{330 m}/₁₀₀

After cross multiplication, we get

14883 × 100 = 330 m

⇒ 330 m = 14883 × 100

⇒ m = ^{14883 × 100}/₃₃₀

⇒ m = ^1488300/₃₃₀ = 4510

⇒ m = 4510

Thus, the Cost Price (CP) = $4510 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) = $14883

And, the profit = 230%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 230% of 100 = 230

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

⇒ Sale Price (SP) = 100 + 230

⇒ Sale Price (SP) = 330

∵ If the Sale Price (SP) is 330, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₃₀

∴ If the Sale Price (SP) is 14883, then the Cost Price (CP)

= ¹⁰⁰/₃₃₀ × 14883

= ^{100 × 14883}/₃₃₀

= ^1488300/₃₃₀ = 4510

Thus, the Cost Price (CP) = $4510 Answer

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

Given, the sale price (SP) = $14883

And, the profit = 230%

Then, the Cost Price (CP) = ?

SP = 330% of CP

⇒ SP = ³³⁰/₁₀₀ × CP

⇒ 14883 = ^{330 CP}/₁₀₀

After cross multiplication

⇒ 14883 × 100 = 330 CP

⇒ 330 CP = 14883 × 100

⇒ CP = ^{14883 × 100}/₃₃₀

⇒ CP = ^1488300/₃₃₀ = 4510

⇒ CP = $4510 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20

(2) Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5

(3) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?

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

(5) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(6) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

(7) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

(8) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.

(9) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

(10) If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.