Profit And Loss
Math MCQs

Question :    Mr. Peter earns a profit of 110% by selling goods for $4431.00. For how much was he purchased those goods?

Correct Answer  2110

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) = $4431

And, the profit = 110%

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 + 110} × 4431

= ^{100 × 4431}/₂₁₀

= ⁴⁴³¹⁰⁰/₂₁₀ = 2110

Thus, the Cost Price (CP) = $2110 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 = 110%

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

= 110% of m

= 110% × m

= ¹¹⁰/₁₀₀ × m

⇒ Profit = ^{110 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 4431 = m + ^{110 m}/₁₀₀

⇒ 4431 = ^{100 m + 110 m}/₁₀₀

⇒ 4431 = ^{210 m}/₁₀₀

After cross multiplication, we get

4431 × 100 = 210 m

⇒ 210 m = 4431 × 100

⇒ m = ^{4431 × 100}/₂₁₀

⇒ m = ⁴⁴³¹⁰⁰/₂₁₀ = 2110

⇒ m = 2110

Thus, the Cost Price (CP) = $2110 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) = $4431

And, the profit = 110%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 110% of 100 = 110

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

⇒ Sale Price (SP) = 100 + 110

⇒ Sale Price (SP) = 210

∵ If the Sale Price (SP) is 210, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₁₀

∴ If the Sale Price (SP) is 4431, then the Cost Price (CP)

= ¹⁰⁰/₂₁₀ × 4431

= ^{100 × 4431}/₂₁₀

= ⁴⁴³¹⁰⁰/₂₁₀ = 2110

Thus, the Cost Price (CP) = $2110 Answer

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

Given, the sale price (SP) = $4431

And, the profit = 110%

Then, the Cost Price (CP) = ?

SP = 210% of CP

⇒ SP = ²¹⁰/₁₀₀ × CP

⇒ 4431 = ^{210 CP}/₁₀₀

After cross multiplication

⇒ 4431 × 100 = 210 CP

⇒ 210 CP = 4431 × 100

⇒ CP = ^{4431 × 100}/₂₁₀

⇒ CP = ⁴⁴³¹⁰⁰/₂₁₀ = 2110

⇒ CP = $2110 Answer

Similar Questions

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(2) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(3) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(4) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

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(6) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(7) Mr. Noah loses 37% by selling an article for $1077.30. For how much should he sell it to get a profit of 36%?

(8) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(9) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

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