Profit And Loss
Math MCQs

Question :    Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

Correct Answer  5310

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) = $19647

And, the profit = 270%

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 + 270} × 19647

= ^{100 × 19647}/₃₇₀

= ^1964700/₃₇₀ = 5310

Thus, the Cost Price (CP) = $5310 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 = 270%

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

= 270% of m

= 270% × m

= ²⁷⁰/₁₀₀ × m

⇒ Profit = ^{270 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 19647 = m + ^{270 m}/₁₀₀

⇒ 19647 = ^{100 m + 270 m}/₁₀₀

⇒ 19647 = ^{370 m}/₁₀₀

After cross multiplication, we get

19647 × 100 = 370 m

⇒ 370 m = 19647 × 100

⇒ m = ^{19647 × 100}/₃₇₀

⇒ m = ^1964700/₃₇₀ = 5310

⇒ m = 5310

Thus, the Cost Price (CP) = $5310 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) = $19647

And, the profit = 270%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 270% of 100 = 270

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

⇒ Sale Price (SP) = 100 + 270

⇒ Sale Price (SP) = 370

∵ If the Sale Price (SP) is 370, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₇₀

∴ If the Sale Price (SP) is 19647, then the Cost Price (CP)

= ¹⁰⁰/₃₇₀ × 19647

= ^{100 × 19647}/₃₇₀

= ^1964700/₃₇₀ = 5310

Thus, the Cost Price (CP) = $5310 Answer

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

Given, the sale price (SP) = $19647

And, the profit = 270%

Then, the Cost Price (CP) = ?

SP = 370% of CP

⇒ SP = ³⁷⁰/₁₀₀ × CP

⇒ 19647 = ^{370 CP}/₁₀₀

After cross multiplication

⇒ 19647 × 100 = 370 CP

⇒ 370 CP = 19647 × 100

⇒ CP = ^{19647 × 100}/₃₇₀

⇒ CP = ^1964700/₃₇₀ = 5310

⇒ CP = $5310 Answer

Similar Questions

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

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(7) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?

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(9) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?

(10) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70