Profit And Loss
Math MCQs

Question :    By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.

Correct Answer  4110

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) = $12741

And, the profit = 210%

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 + 210} × 12741

= ^{100 × 12741}/₃₁₀

= ^1274100/₃₁₀ = 4110

Thus, the Cost Price (CP) = $4110 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 = 210%

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

= 210% of m

= 210% × m

= ²¹⁰/₁₀₀ × m

⇒ Profit = ^{210 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 12741 = m + ^{210 m}/₁₀₀

⇒ 12741 = ^{100 m + 210 m}/₁₀₀

⇒ 12741 = ^{310 m}/₁₀₀

After cross multiplication, we get

12741 × 100 = 310 m

⇒ 310 m = 12741 × 100

⇒ m = ^{12741 × 100}/₃₁₀

⇒ m = ^1274100/₃₁₀ = 4110

⇒ m = 4110

Thus, the Cost Price (CP) = $4110 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) = $12741

And, the profit = 210%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 210% of 100 = 210

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

⇒ Sale Price (SP) = 100 + 210

⇒ Sale Price (SP) = 310

∵ If the Sale Price (SP) is 310, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₁₀

∴ If the Sale Price (SP) is 12741, then the Cost Price (CP)

= ¹⁰⁰/₃₁₀ × 12741

= ^{100 × 12741}/₃₁₀

= ^1274100/₃₁₀ = 4110

Thus, the Cost Price (CP) = $4110 Answer

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

Given, the sale price (SP) = $12741

And, the profit = 210%

Then, the Cost Price (CP) = ?

SP = 310% of CP

⇒ SP = ³¹⁰/₁₀₀ × CP

⇒ 12741 = ^{310 CP}/₁₀₀

After cross multiplication

⇒ 12741 × 100 = 310 CP

⇒ 310 CP = 12741 × 100

⇒ CP = ^{12741 × 100}/₃₁₀

⇒ CP = ^1274100/₃₁₀ = 4110

⇒ CP = $4110 Answer

Similar Questions

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(2) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(3) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?

(4) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5

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(6) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

(7) Find the cost price, if a trader gets a loss of 59% by selling five TV sets for $4760.10

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

(9) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(10) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?