Profit And Loss
Math MCQs

Question :    Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

Correct Answer  2010

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) = $4120.5

And, the profit = 105%

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 + 105} × 4120.5

= ^{100 × 4120.5}/₂₀₅

= ⁴¹²⁰⁵⁰/₂₀₅ = 2010

Thus, the Cost Price (CP) = $2010 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 = 105%

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

= 105% of m

= 105% × m

= ¹⁰⁵/₁₀₀ × m

⇒ Profit = ^{105 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 4120.5 = m + ^{105 m}/₁₀₀

⇒ 4120.5 = ^{100 m + 105 m}/₁₀₀

⇒ 4120.5 = ^{205 m}/₁₀₀

After cross multiplication, we get

4120.5 × 100 = 205 m

⇒ 205 m = 4120.5 × 100

⇒ m = ^{4120.5 × 100}/₂₀₅

⇒ m = ⁴¹²⁰⁵⁰/₂₀₅ = 2010

⇒ m = 2010

Thus, the Cost Price (CP) = $2010 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) = $4120.5

And, the profit = 105%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 105% of 100 = 105

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

⇒ Sale Price (SP) = 100 + 105

⇒ Sale Price (SP) = 205

∵ If the Sale Price (SP) is 205, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₀₅

∴ If the Sale Price (SP) is 4120.5, then the Cost Price (CP)

= ¹⁰⁰/₂₀₅ × 4120.5

= ^{100 × 4120.5}/₂₀₅

= ⁴¹²⁰⁵⁰/₂₀₅ = 2010

Thus, the Cost Price (CP) = $2010 Answer

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

Given, the sale price (SP) = $4120.5

And, the profit = 105%

Then, the Cost Price (CP) = ?

SP = 205% of CP

⇒ SP = ²⁰⁵/₁₀₀ × CP

⇒ 4120.5 = ^{205 CP}/₁₀₀

After cross multiplication

⇒ 4120.5 × 100 = 205 CP

⇒ 205 CP = 4120.5 × 100

⇒ CP = ^{4120.5 × 100}/₂₀₅

⇒ CP = ⁴¹²⁰⁵⁰/₂₀₅ = 2010

⇒ CP = $2010 Answer

Similar Questions

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(2) Mr. Steven loses 92% by selling an article for $356.80. For how much should he sell it to get a profit of 91%?

(3) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

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(7) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

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