Profit And Loss
Math MCQs

Question :    By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price

Correct Answer  4410

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) = $14332.5

And, the profit = 225%

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 + 225} × 14332.5

= ^{100 × 14332.5}/₃₂₅

= ^1433250/₃₂₅ = 4410

Thus, the Cost Price (CP) = $4410 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 = 225%

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

= 225% of m

= 225% × m

= ²²⁵/₁₀₀ × m

⇒ Profit = ^{225 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 14332.5 = m + ^{225 m}/₁₀₀

⇒ 14332.5 = ^{100 m + 225 m}/₁₀₀

⇒ 14332.5 = ^{325 m}/₁₀₀

After cross multiplication, we get

14332.5 × 100 = 325 m

⇒ 325 m = 14332.5 × 100

⇒ m = ^{14332.5 × 100}/₃₂₅

⇒ m = ^1433250/₃₂₅ = 4410

⇒ m = 4410

Thus, the Cost Price (CP) = $4410 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) = $14332.5

And, the profit = 225%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 225% of 100 = 225

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

⇒ Sale Price (SP) = 100 + 225

⇒ Sale Price (SP) = 325

∵ If the Sale Price (SP) is 325, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₂₅

∴ If the Sale Price (SP) is 14332.5, then the Cost Price (CP)

= ¹⁰⁰/₃₂₅ × 14332.5

= ^{100 × 14332.5}/₃₂₅

= ^1433250/₃₂₅ = 4410

Thus, the Cost Price (CP) = $4410 Answer

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

Given, the sale price (SP) = $14332.5

And, the profit = 225%

Then, the Cost Price (CP) = ?

SP = 325% of CP

⇒ SP = ³²⁵/₁₀₀ × CP

⇒ 14332.5 = ^{325 CP}/₁₀₀

After cross multiplication

⇒ 14332.5 × 100 = 325 CP

⇒ 325 CP = 14332.5 × 100

⇒ CP = ^{14332.5 × 100}/₃₂₅

⇒ CP = ^1433250/₃₂₅ = 4410

⇒ CP = $4410 Answer

Similar Questions

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(2) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?

(3) After selling a furniture for $481.60 a shopkeeper gets a loss of 14%. In order to get a profit of 13% he should sell in for how much?

(4) Find the cost price, if a trader gets a loss of 73% by selling 100 bags of apples for $3890.70 then find the cost price of the apples.

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(7) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

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(9) A trader earns a profit of 170% by selling an article for $8937. Find the cost price.

(10) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?