Profit And Loss
Math MCQs

Question :    Find the cost price, if Mrs. Barbara earns a profit of 275% by selling some items for $20287.50

Correct Answer  5410

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) = $20287.5

And, the profit = 275%

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 + 275} × 20287.5

= ^{100 × 20287.5}/₃₇₅

= ^2028750/₃₇₅ = 5410

Thus, the Cost Price (CP) = $5410 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 = 275%

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

= 275% of m

= 275% × m

= ²⁷⁵/₁₀₀ × m

⇒ Profit = ^{275 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 20287.5 = m + ^{275 m}/₁₀₀

⇒ 20287.5 = ^{100 m + 275 m}/₁₀₀

⇒ 20287.5 = ^{375 m}/₁₀₀

After cross multiplication, we get

20287.5 × 100 = 375 m

⇒ 375 m = 20287.5 × 100

⇒ m = ^{20287.5 × 100}/₃₇₅

⇒ m = ^2028750/₃₇₅ = 5410

⇒ m = 5410

Thus, the Cost Price (CP) = $5410 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) = $20287.5

And, the profit = 275%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 275% of 100 = 275

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

⇒ Sale Price (SP) = 100 + 275

⇒ Sale Price (SP) = 375

∵ If the Sale Price (SP) is 375, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₇₅

∴ If the Sale Price (SP) is 20287.5, then the Cost Price (CP)

= ¹⁰⁰/₃₇₅ × 20287.5

= ^{100 × 20287.5}/₃₇₅

= ^2028750/₃₇₅ = 5410

Thus, the Cost Price (CP) = $5410 Answer

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

Given, the sale price (SP) = $20287.5

And, the profit = 275%

Then, the Cost Price (CP) = ?

SP = 375% of CP

⇒ SP = ³⁷⁵/₁₀₀ × CP

⇒ 20287.5 = ^{375 CP}/₁₀₀

After cross multiplication

⇒ 20287.5 × 100 = 375 CP

⇒ 375 CP = 20287.5 × 100

⇒ CP = ^{20287.5 × 100}/₃₇₅

⇒ CP = ^2028750/₃₇₅ = 5410

⇒ CP = $5410 Answer

Similar Questions

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(2) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?

(3) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(4) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

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(7) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(8) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90

(9) If Mr. Jobby buys 18 kiwis for $1 and sells them at a rate of 17 per $1 then what would be the profit percent?.

(10) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?