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) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.

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

(3) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?

(4) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?

(5) Find the cost price, if a vendor gets a loss of 34% by selling some articles for $4362.60

(6) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

(7) James loses 66% by selling an article for $1074.40. For how much should he sell it to get a profit of 65%?

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

(9) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(10) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.