Profit And Loss
Math MCQs

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

Correct Answer  3310

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) = $8937

And, the profit = 170%

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 + 170} × 8937

= ^{100 × 8937}/₂₇₀

= ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

Thus, the Cost Price (CP) = $3310 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 = 170%

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

= 170% of m

= 170% × m

= ¹⁷⁰/₁₀₀ × m

⇒ Profit = ^{170 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 8937 = m + ^{170 m}/₁₀₀

⇒ 8937 = ^{100 m + 170 m}/₁₀₀

⇒ 8937 = ^{270 m}/₁₀₀

After cross multiplication, we get

8937 × 100 = 270 m

⇒ 270 m = 8937 × 100

⇒ m = ^{8937 × 100}/₂₇₀

⇒ m = ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

⇒ m = 3310

Thus, the Cost Price (CP) = $3310 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) = $8937

And, the profit = 170%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 170% of 100 = 170

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

⇒ Sale Price (SP) = 100 + 170

⇒ Sale Price (SP) = 270

∵ If the Sale Price (SP) is 270, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₇₀

∴ If the Sale Price (SP) is 8937, then the Cost Price (CP)

= ¹⁰⁰/₂₇₀ × 8937

= ^{100 × 8937}/₂₇₀

= ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

Thus, the Cost Price (CP) = $3310 Answer

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

Given, the sale price (SP) = $8937

And, the profit = 170%

Then, the Cost Price (CP) = ?

SP = 270% of CP

⇒ SP = ²⁷⁰/₁₀₀ × CP

⇒ 8937 = ^{270 CP}/₁₀₀

After cross multiplication

⇒ 8937 × 100 = 270 CP

⇒ 270 CP = 8937 × 100

⇒ CP = ^{8937 × 100}/₂₇₀

⇒ CP = ⁸⁹³⁷⁰⁰/₂₇₀ = 3310

⇒ CP = $3310 Answer

Similar Questions

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(2) Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

(3) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.

(4) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

(5) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(6) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(7) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718

(8) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

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

(10) Find the cost price, if a share broker gets a loss of 27% by selling 200 shares for $3803.30.