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 shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(2) To earn a profit of 7% Mr. Robert should sell his article for how much if he gets a loss of 8% by selling it for $239.20?

(3) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

(4) If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

(5) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(6) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(7) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

(8) Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.

(9) Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

(10) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price