Profit And Loss
Math MCQs

Question :    After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

Correct Answer  4210

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) = $13261.5

And, the profit = 215%

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 + 215} × 13261.5

= ^{100 × 13261.5}/₃₁₅

= ^1326150/₃₁₅ = 4210

Thus, the Cost Price (CP) = $4210 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 = 215%

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

= 215% of m

= 215% × m

= ²¹⁵/₁₀₀ × m

⇒ Profit = ^{215 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 13261.5 = m + ^{215 m}/₁₀₀

⇒ 13261.5 = ^{100 m + 215 m}/₁₀₀

⇒ 13261.5 = ^{315 m}/₁₀₀

After cross multiplication, we get

13261.5 × 100 = 315 m

⇒ 315 m = 13261.5 × 100

⇒ m = ^{13261.5 × 100}/₃₁₅

⇒ m = ^1326150/₃₁₅ = 4210

⇒ m = 4210

Thus, the Cost Price (CP) = $4210 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) = $13261.5

And, the profit = 215%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 215% of 100 = 215

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

⇒ Sale Price (SP) = 100 + 215

⇒ Sale Price (SP) = 315

∵ If the Sale Price (SP) is 315, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₁₅

∴ If the Sale Price (SP) is 13261.5, then the Cost Price (CP)

= ¹⁰⁰/₃₁₅ × 13261.5

= ^{100 × 13261.5}/₃₁₅

= ^1326150/₃₁₅ = 4210

Thus, the Cost Price (CP) = $4210 Answer

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

Given, the sale price (SP) = $13261.5

And, the profit = 215%

Then, the Cost Price (CP) = ?

SP = 315% of CP

⇒ SP = ³¹⁵/₁₀₀ × CP

⇒ 13261.5 = ^{315 CP}/₁₀₀

After cross multiplication

⇒ 13261.5 × 100 = 315 CP

⇒ 315 CP = 13261.5 × 100

⇒ CP = ^{13261.5 × 100}/₃₁₅

⇒ CP = ^1326150/₃₁₅ = 4210

⇒ CP = $4210 Answer

Similar Questions

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

(2) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

(3) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?

(4) 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?

(5) If a trader earns a profit of 10% by selling rice for $121 per kg, then find the cost price of the rice

(6) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

(7) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(8) Find the cost price, if a trader gets a loss of 73% by selling 100 bags of apples for $3890.70 then find the cost price of the apples.

(9) Find the cost price, if a trader gets a loss of 54% by selling 100 bags of mobile covers for $4880.60

(10) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.