Profit And Loss
Math MCQs

Question :    Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%

Correct Answer  4310

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) = $13792

And, the profit = 220%

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 + 220} × 13792

= ^{100 × 13792}/₃₂₀

= ^1379200/₃₂₀ = 4310

Thus, the Cost Price (CP) = $4310 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 = 220%

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

= 220% of m

= 220% × m

= ²²⁰/₁₀₀ × m

⇒ Profit = ^{220 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 13792 = m + ^{220 m}/₁₀₀

⇒ 13792 = ^{100 m + 220 m}/₁₀₀

⇒ 13792 = ^{320 m}/₁₀₀

After cross multiplication, we get

13792 × 100 = 320 m

⇒ 320 m = 13792 × 100

⇒ m = ^{13792 × 100}/₃₂₀

⇒ m = ^1379200/₃₂₀ = 4310

⇒ m = 4310

Thus, the Cost Price (CP) = $4310 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) = $13792

And, the profit = 220%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 220% of 100 = 220

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

⇒ Sale Price (SP) = 100 + 220

⇒ Sale Price (SP) = 320

∵ If the Sale Price (SP) is 320, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₂₀

∴ If the Sale Price (SP) is 13792, then the Cost Price (CP)

= ¹⁰⁰/₃₂₀ × 13792

= ^{100 × 13792}/₃₂₀

= ^1379200/₃₂₀ = 4310

Thus, the Cost Price (CP) = $4310 Answer

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

Given, the sale price (SP) = $13792

And, the profit = 220%

Then, the Cost Price (CP) = ?

SP = 320% of CP

⇒ SP = ³²⁰/₁₀₀ × CP

⇒ 13792 = ^{320 CP}/₁₀₀

After cross multiplication

⇒ 13792 × 100 = 320 CP

⇒ 320 CP = 13792 × 100

⇒ CP = ^{13792 × 100}/₃₂₀

⇒ CP = ^1379200/₃₂₀ = 4310

⇒ CP = $4310 Answer

Similar Questions

(1) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?

(2) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(3) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70

(4) A trader earns a profit of 205% by selling some articles for $12230.50. What was the cost price?

(5) Find the cost price, if a trader gets a loss of 57% by selling a TV set for $4820.30

(6) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

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

(8) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

(9) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?

(10) Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.