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) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(2) Peter loses 3% by selling an article for $9.70. For how much should he sell it to get a profit of 2%?

(3) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?

(4) Find the cost price, if a broker earns a profit of 370% by selling an old house for $34357

(5) For how much should Mr. Bose sell his furniture to get a profit of 28%, if he loses 29% by selling it for $930.10?

(6) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

(7) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

(8) If Boby buys 69 pencils for $1 and sells them at a rate of 68 per $1 then, find the earnings in percentage.

(9) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(10) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.