Profit And Loss
Math MCQs

Question :    After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

Correct Answer  5710

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) = $22269

And, the profit = 290%

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 + 290} × 22269

= ^{100 × 22269}/₃₉₀

= ^2226900/₃₉₀ = 5710

Thus, the Cost Price (CP) = $5710 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 = 290%

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

= 290% of m

= 290% × m

= ²⁹⁰/₁₀₀ × m

⇒ Profit = ^{290 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 22269 = m + ^{290 m}/₁₀₀

⇒ 22269 = ^{100 m + 290 m}/₁₀₀

⇒ 22269 = ^{390 m}/₁₀₀

After cross multiplication, we get

22269 × 100 = 390 m

⇒ 390 m = 22269 × 100

⇒ m = ^{22269 × 100}/₃₉₀

⇒ m = ^2226900/₃₉₀ = 5710

⇒ m = 5710

Thus, the Cost Price (CP) = $5710 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) = $22269

And, the profit = 290%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 290% of 100 = 290

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

⇒ Sale Price (SP) = 100 + 290

⇒ Sale Price (SP) = 390

∵ If the Sale Price (SP) is 390, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₉₀

∴ If the Sale Price (SP) is 22269, then the Cost Price (CP)

= ¹⁰⁰/₃₉₀ × 22269

= ^{100 × 22269}/₃₉₀

= ^2226900/₃₉₀ = 5710

Thus, the Cost Price (CP) = $5710 Answer

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

Given, the sale price (SP) = $22269

And, the profit = 290%

Then, the Cost Price (CP) = ?

SP = 390% of CP

⇒ SP = ³⁹⁰/₁₀₀ × CP

⇒ 22269 = ^{390 CP}/₁₀₀

After cross multiplication

⇒ 22269 × 100 = 390 CP

⇒ 390 CP = 22269 × 100

⇒ CP = ^{22269 × 100}/₃₉₀

⇒ CP = ^2226900/₃₉₀ = 5710

⇒ CP = $5710 Answer

Similar Questions

(1) Find the cost price, if Mrs. Olivia earns a profit of 160% by selling some articles for $8086

(2) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

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

(4) if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

(5) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(6) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(7) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

(8) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(9) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(10) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.