Profit And Loss
Math MCQs

Question :    What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50

Correct Answer  3010

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) = $7675.5

And, the profit = 155%

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 + 155} × 7675.5

= ^{100 × 7675.5}/₂₅₅

= ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

Thus, the Cost Price (CP) = $3010 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 = 155%

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

= 155% of m

= 155% × m

= ¹⁵⁵/₁₀₀ × m

⇒ Profit = ^{155 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 7675.5 = m + ^{155 m}/₁₀₀

⇒ 7675.5 = ^{100 m + 155 m}/₁₀₀

⇒ 7675.5 = ^{255 m}/₁₀₀

After cross multiplication, we get

7675.5 × 100 = 255 m

⇒ 255 m = 7675.5 × 100

⇒ m = ^{7675.5 × 100}/₂₅₅

⇒ m = ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

⇒ m = 3010

Thus, the Cost Price (CP) = $3010 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) = $7675.5

And, the profit = 155%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 155% of 100 = 155

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

⇒ Sale Price (SP) = 100 + 155

⇒ Sale Price (SP) = 255

∵ If the Sale Price (SP) is 255, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₅₅

∴ If the Sale Price (SP) is 7675.5, then the Cost Price (CP)

= ¹⁰⁰/₂₅₅ × 7675.5

= ^{100 × 7675.5}/₂₅₅

= ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

Thus, the Cost Price (CP) = $3010 Answer

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

Given, the sale price (SP) = $7675.5

And, the profit = 155%

Then, the Cost Price (CP) = ?

SP = 255% of CP

⇒ SP = ²⁵⁵/₁₀₀ × CP

⇒ 7675.5 = ^{255 CP}/₁₀₀

After cross multiplication

⇒ 7675.5 × 100 = 255 CP

⇒ 255 CP = 7675.5 × 100

⇒ CP = ^{7675.5 × 100}/₂₅₅

⇒ CP = ⁷⁶⁷⁵⁵⁰/₂₅₅ = 3010

⇒ CP = $3010 Answer

Similar Questions

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(2) The cost price of an article is $12, and the sale price is $15. Find the profit and profit percent.

(3) William loses 72% by selling an article for $968.80. For how much should he sell it to get a profit of 71%?

(4) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

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

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(7) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

(8) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

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(10) James loses 66% by selling an article for $1074.40. For how much should he sell it to get a profit of 65%?