Profit And Loss
Math MCQs

Question :    If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

Correct Answer  810

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) = $1174.5

And, the profit = 45%

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 + 45} × 1174.5

= ^{100 × 1174.5}/₁₄₅

= ¹¹⁷⁴⁵⁰/₁₄₅ = 810

Thus, the Cost Price (CP) = $810 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 = 45%

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

= 45% of m

= 45% × m

= ⁴⁵/₁₀₀ × m

⇒ Profit = ^{45 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1174.5 = m + ^{45 m}/₁₀₀

⇒ 1174.5 = ^{100 m + 45 m}/₁₀₀

⇒ 1174.5 = ^{145 m}/₁₀₀

After cross multiplication, we get

1174.5 × 100 = 145 m

⇒ 145 m = 1174.5 × 100

⇒ m = ^{1174.5 × 100}/₁₄₅

⇒ m = ¹¹⁷⁴⁵⁰/₁₄₅ = 810

⇒ m = 810

Thus, the Cost Price (CP) = $810 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) = $1174.5

And, the profit = 45%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 45% of 100 = 45

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

⇒ Sale Price (SP) = 100 + 45

⇒ Sale Price (SP) = 145

∵ If the Sale Price (SP) is 145, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₄₅

∴ If the Sale Price (SP) is 1174.5, then the Cost Price (CP)

= ¹⁰⁰/₁₄₅ × 1174.5

= ^{100 × 1174.5}/₁₄₅

= ¹¹⁷⁴⁵⁰/₁₄₅ = 810

Thus, the Cost Price (CP) = $810 Answer

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

Given, the sale price (SP) = $1174.5

And, the profit = 45%

Then, the Cost Price (CP) = ?

SP = 145% of CP

⇒ SP = ¹⁴⁵/₁₀₀ × CP

⇒ 1174.5 = ^{145 CP}/₁₀₀

After cross multiplication

⇒ 1174.5 × 100 = 145 CP

⇒ 145 CP = 1174.5 × 100

⇒ CP = ^{1174.5 × 100}/₁₄₅

⇒ CP = ¹¹⁷⁴⁵⁰/₁₄₅ = 810

⇒ CP = $810 Answer

Similar Questions

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(2) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?

(3) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(4) Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.

(5) By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

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(7) Mr. Steven loses 92% by selling an article for $356.80. For how much should he sell it to get a profit of 91%?

(8) Mr. Henry loses 26% by selling an article for $858.4. For how much should he sell it to get a profit of 25%?

(9) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70

(10) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?