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

(1) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.

(2) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?

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

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

(5) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(6) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(7) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.

(8) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(9) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?

(10) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?