Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

Correct Answer  10

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) = $10.5

And, the profit = 5%

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 + 5} × 10.5

= ^{100 × 10.5}/₁₀₅

= ¹⁰⁵⁰/₁₀₅ = 10

Thus, the Cost Price (CP) = $10 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 = 5%

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

= 5% of m

= 5% × m

= ⁵/₁₀₀ × m

⇒ Profit = ^{5 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 10.5 = m + ^{5 m}/₁₀₀

⇒ 10.5 = ^{100 m + 5 m}/₁₀₀

⇒ 10.5 = ^{105 m}/₁₀₀

After cross multiplication, we get

10.5 × 100 = 105 m

⇒ 105 m = 10.5 × 100

⇒ m = ^{10.5 × 100}/₁₀₅

⇒ m = ¹⁰⁵⁰/₁₀₅ = 10

⇒ m = 10

Thus, the Cost Price (CP) = $10 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) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 5% of 100 = 5

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

⇒ Sale Price (SP) = 100 + 5

⇒ Sale Price (SP) = 105

∵ If the Sale Price (SP) is 105, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₀₅

∴ If the Sale Price (SP) is 10.5, then the Cost Price (CP)

= ¹⁰⁰/₁₀₅ × 10.5

= ^{100 × 10.5}/₁₀₅

= ¹⁰⁵⁰/₁₀₅ = 10

Thus, the Cost Price (CP) = $10 Answer

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

Given, the sale price (SP) = $10.5

And, the profit = 5%

Then, the Cost Price (CP) = ?

SP = 105% of CP

⇒ SP = ¹⁰⁵/₁₀₀ × CP

⇒ 10.5 = ^{105 CP}/₁₀₀

After cross multiplication

⇒ 10.5 × 100 = 105 CP

⇒ 105 CP = 10.5 × 100

⇒ CP = ^{10.5 × 100}/₁₀₅

⇒ CP = ¹⁰⁵⁰/₁₀₅ = 10

⇒ CP = $10 Answer

Similar Questions

(1) Mr. Donald loses 88% by selling an article for $511.20. For how much should he sell it to get a profit of 87%?

(2) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

(3) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(4) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

(5) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(6) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

(7) Find the earnings percentage if a vendor buys 49 articles for $1 and sells 48 articles for $1.

(8) If Robert purchased a TV set in an auction at $250 and sold it at $300, then calculate the profit earned and profit percent in this sale.

(9) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70

(10) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.