Profit And Loss
Math MCQs

Question :    In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

Correct Answer  6410

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) = $27242.5

And, the profit = 325%

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 + 325} × 27242.5

= ^{100 × 27242.5}/₄₂₅

= ^2724250/₄₂₅ = 6410

Thus, the Cost Price (CP) = $6410 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 = 325%

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

= 325% of m

= 325% × m

= ³²⁵/₁₀₀ × m

⇒ Profit = ^{325 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 27242.5 = m + ^{325 m}/₁₀₀

⇒ 27242.5 = ^{100 m + 325 m}/₁₀₀

⇒ 27242.5 = ^{425 m}/₁₀₀

After cross multiplication, we get

27242.5 × 100 = 425 m

⇒ 425 m = 27242.5 × 100

⇒ m = ^{27242.5 × 100}/₄₂₅

⇒ m = ^2724250/₄₂₅ = 6410

⇒ m = 6410

Thus, the Cost Price (CP) = $6410 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) = $27242.5

And, the profit = 325%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 325% of 100 = 325

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

⇒ Sale Price (SP) = 100 + 325

⇒ Sale Price (SP) = 425

∵ If the Sale Price (SP) is 425, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₂₅

∴ If the Sale Price (SP) is 27242.5, then the Cost Price (CP)

= ¹⁰⁰/₄₂₅ × 27242.5

= ^{100 × 27242.5}/₄₂₅

= ^2724250/₄₂₅ = 6410

Thus, the Cost Price (CP) = $6410 Answer

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

Given, the sale price (SP) = $27242.5

And, the profit = 325%

Then, the Cost Price (CP) = ?

SP = 425% of CP

⇒ SP = ⁴²⁵/₁₀₀ × CP

⇒ 27242.5 = ^{425 CP}/₁₀₀

After cross multiplication

⇒ 27242.5 × 100 = 425 CP

⇒ 425 CP = 27242.5 × 100

⇒ CP = ^{27242.5 × 100}/₄₂₅

⇒ CP = ^2724250/₄₂₅ = 6410

⇒ CP = $6410 Answer

Similar Questions

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(2) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

(3) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(4) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

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(7) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(8) A trader loses 52% by selling an article for $1180.80. For how much should he sell it to get a profit of 51%?

(9) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

(10) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?