Profit And Loss
Math MCQs

Question :    By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

Correct Answer  4610

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) = $15443.5

And, the profit = 235%

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 + 235} × 15443.5

= ^{100 × 15443.5}/₃₃₅

= ^1544350/₃₃₅ = 4610

Thus, the Cost Price (CP) = $4610 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 = 235%

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

= 235% of m

= 235% × m

= ²³⁵/₁₀₀ × m

⇒ Profit = ^{235 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 15443.5 = m + ^{235 m}/₁₀₀

⇒ 15443.5 = ^{100 m + 235 m}/₁₀₀

⇒ 15443.5 = ^{335 m}/₁₀₀

After cross multiplication, we get

15443.5 × 100 = 335 m

⇒ 335 m = 15443.5 × 100

⇒ m = ^{15443.5 × 100}/₃₃₅

⇒ m = ^1544350/₃₃₅ = 4610

⇒ m = 4610

Thus, the Cost Price (CP) = $4610 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) = $15443.5

And, the profit = 235%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 235% of 100 = 235

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

⇒ Sale Price (SP) = 100 + 235

⇒ Sale Price (SP) = 335

∵ If the Sale Price (SP) is 335, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₃₅

∴ If the Sale Price (SP) is 15443.5, then the Cost Price (CP)

= ¹⁰⁰/₃₃₅ × 15443.5

= ^{100 × 15443.5}/₃₃₅

= ^1544350/₃₃₅ = 4610

Thus, the Cost Price (CP) = $4610 Answer

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

Given, the sale price (SP) = $15443.5

And, the profit = 235%

Then, the Cost Price (CP) = ?

SP = 335% of CP

⇒ SP = ³³⁵/₁₀₀ × CP

⇒ 15443.5 = ^{335 CP}/₁₀₀

After cross multiplication

⇒ 15443.5 × 100 = 335 CP

⇒ 335 CP = 15443.5 × 100

⇒ CP = ^{15443.5 × 100}/₃₃₅

⇒ CP = ^1544350/₃₃₅ = 4610

⇒ CP = $4610 Answer

Similar Questions

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(2) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(3) Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

(4) Mrs. Julie buys 16 oranges for $1 and sells 15 oranges for $1. What is her profit percent in this sale?

(5) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(6) Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.

(7) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(8) Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??

(9) Find the cost price, if a trader gets a loss of 73% by selling 100 bags of apples for $3890.70 then find the cost price of the apples.

(10) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?