Profit And Loss
Math MCQs

Question :    Find the cost price, if a house broker earns a profit of 365% by selling a plot for $33526.5

Correct Answer  7210

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) = $33526.5

And, the profit = 365%

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 + 365} × 33526.5

= ^{100 × 33526.5}/₄₆₅

= ^3352650/₄₆₅ = 7210

Thus, the Cost Price (CP) = $7210 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 = 365%

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

= 365% of m

= 365% × m

= ³⁶⁵/₁₀₀ × m

⇒ Profit = ^{365 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 33526.5 = m + ^{365 m}/₁₀₀

⇒ 33526.5 = ^{100 m + 365 m}/₁₀₀

⇒ 33526.5 = ^{465 m}/₁₀₀

After cross multiplication, we get

33526.5 × 100 = 465 m

⇒ 465 m = 33526.5 × 100

⇒ m = ^{33526.5 × 100}/₄₆₅

⇒ m = ^3352650/₄₆₅ = 7210

⇒ m = 7210

Thus, the Cost Price (CP) = $7210 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) = $33526.5

And, the profit = 365%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 365% of 100 = 365

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

⇒ Sale Price (SP) = 100 + 365

⇒ Sale Price (SP) = 465

∵ If the Sale Price (SP) is 465, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₆₅

∴ If the Sale Price (SP) is 33526.5, then the Cost Price (CP)

= ¹⁰⁰/₄₆₅ × 33526.5

= ^{100 × 33526.5}/₄₆₅

= ^3352650/₄₆₅ = 7210

Thus, the Cost Price (CP) = $7210 Answer

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

Given, the sale price (SP) = $33526.5

And, the profit = 365%

Then, the Cost Price (CP) = ?

SP = 465% of CP

⇒ SP = ⁴⁶⁵/₁₀₀ × CP

⇒ 33526.5 = ^{465 CP}/₁₀₀

After cross multiplication

⇒ 33526.5 × 100 = 465 CP

⇒ 465 CP = 33526.5 × 100

⇒ CP = ^{33526.5 × 100}/₄₆₅

⇒ CP = ^3352650/₄₆₅ = 7210

⇒ CP = $7210 Answer

Similar Questions

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(3) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?

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(8) Oliver loses 35% by selling an article for $1046.50. For how much should he sell it to get a profit of 34%?

(9) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

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