Profit And Loss
Math MCQs

Question :    If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.

Correct Answer  5110

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) = $18396

And, the profit = 260%

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 + 260} × 18396

= ^{100 × 18396}/₃₆₀

= ^1839600/₃₆₀ = 5110

Thus, the Cost Price (CP) = $5110 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 = 260%

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

= 260% of m

= 260% × m

= ²⁶⁰/₁₀₀ × m

⇒ Profit = ^{260 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 18396 = m + ^{260 m}/₁₀₀

⇒ 18396 = ^{100 m + 260 m}/₁₀₀

⇒ 18396 = ^{360 m}/₁₀₀

After cross multiplication, we get

18396 × 100 = 360 m

⇒ 360 m = 18396 × 100

⇒ m = ^{18396 × 100}/₃₆₀

⇒ m = ^1839600/₃₆₀ = 5110

⇒ m = 5110

Thus, the Cost Price (CP) = $5110 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) = $18396

And, the profit = 260%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 260% of 100 = 260

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

⇒ Sale Price (SP) = 100 + 260

⇒ Sale Price (SP) = 360

∵ If the Sale Price (SP) is 360, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₆₀

∴ If the Sale Price (SP) is 18396, then the Cost Price (CP)

= ¹⁰⁰/₃₆₀ × 18396

= ^{100 × 18396}/₃₆₀

= ^1839600/₃₆₀ = 5110

Thus, the Cost Price (CP) = $5110 Answer

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

Given, the sale price (SP) = $18396

And, the profit = 260%

Then, the Cost Price (CP) = ?

SP = 360% of CP

⇒ SP = ³⁶⁰/₁₀₀ × CP

⇒ 18396 = ^{360 CP}/₁₀₀

After cross multiplication

⇒ 18396 × 100 = 360 CP

⇒ 360 CP = 18396 × 100

⇒ CP = ^{18396 × 100}/₃₆₀

⇒ CP = ^1839600/₃₆₀ = 5110

⇒ CP = $5110 Answer

Similar Questions

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(8) Mr. Steven loses 94% by selling an article for $273.60. For how much should he sell it to get a profit of 93%?

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

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