Profit And Loss
Math MCQs

Question :    After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

Correct Answer  2710

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) = $6504

And, the profit = 140%

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 + 140} × 6504

= ^{100 × 6504}/₂₄₀

= ⁶⁵⁰⁴⁰⁰/₂₄₀ = 2710

Thus, the Cost Price (CP) = $2710 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 = 140%

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

= 140% of m

= 140% × m

= ¹⁴⁰/₁₀₀ × m

⇒ Profit = ^{140 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 6504 = m + ^{140 m}/₁₀₀

⇒ 6504 = ^{100 m + 140 m}/₁₀₀

⇒ 6504 = ^{240 m}/₁₀₀

After cross multiplication, we get

6504 × 100 = 240 m

⇒ 240 m = 6504 × 100

⇒ m = ^{6504 × 100}/₂₄₀

⇒ m = ⁶⁵⁰⁴⁰⁰/₂₄₀ = 2710

⇒ m = 2710

Thus, the Cost Price (CP) = $2710 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) = $6504

And, the profit = 140%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 140% of 100 = 140

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

⇒ Sale Price (SP) = 100 + 140

⇒ Sale Price (SP) = 240

∵ If the Sale Price (SP) is 240, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₄₀

∴ If the Sale Price (SP) is 6504, then the Cost Price (CP)

= ¹⁰⁰/₂₄₀ × 6504

= ^{100 × 6504}/₂₄₀

= ⁶⁵⁰⁴⁰⁰/₂₄₀ = 2710

Thus, the Cost Price (CP) = $2710 Answer

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

Given, the sale price (SP) = $6504

And, the profit = 140%

Then, the Cost Price (CP) = ?

SP = 240% of CP

⇒ SP = ²⁴⁰/₁₀₀ × CP

⇒ 6504 = ^{240 CP}/₁₀₀

After cross multiplication

⇒ 6504 × 100 = 240 CP

⇒ 240 CP = 6504 × 100

⇒ CP = ^{6504 × 100}/₂₄₀

⇒ CP = ⁶⁵⁰⁴⁰⁰/₂₄₀ = 2710

⇒ CP = $2710 Answer

Similar Questions

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(2) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

(3) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(4) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?

(5) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?

(6) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30

(7) A shopkeeper gets a loss of 5% by selling some fruits for $769.50. Find the cost price of the furits.

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

(9) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?

(10) A shopkeeper loses 22% by selling an article for $748.80. For how much should he sell it to get a profit of 21%?