Profit And Loss
Math MCQs

Question :    If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

Correct Answer  5010

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) = $17785.5

And, the profit = 255%

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 + 255} × 17785.5

= ^{100 × 17785.5}/₃₅₅

= ^1778550/₃₅₅ = 5010

Thus, the Cost Price (CP) = $5010 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 = 255%

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

= 255% of m

= 255% × m

= ²⁵⁵/₁₀₀ × m

⇒ Profit = ^{255 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 17785.5 = m + ^{255 m}/₁₀₀

⇒ 17785.5 = ^{100 m + 255 m}/₁₀₀

⇒ 17785.5 = ^{355 m}/₁₀₀

After cross multiplication, we get

17785.5 × 100 = 355 m

⇒ 355 m = 17785.5 × 100

⇒ m = ^{17785.5 × 100}/₃₅₅

⇒ m = ^1778550/₃₅₅ = 5010

⇒ m = 5010

Thus, the Cost Price (CP) = $5010 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) = $17785.5

And, the profit = 255%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 255% of 100 = 255

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

⇒ Sale Price (SP) = 100 + 255

⇒ Sale Price (SP) = 355

∵ If the Sale Price (SP) is 355, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₅₅

∴ If the Sale Price (SP) is 17785.5, then the Cost Price (CP)

= ¹⁰⁰/₃₅₅ × 17785.5

= ^{100 × 17785.5}/₃₅₅

= ^1778550/₃₅₅ = 5010

Thus, the Cost Price (CP) = $5010 Answer

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

Given, the sale price (SP) = $17785.5

And, the profit = 255%

Then, the Cost Price (CP) = ?

SP = 355% of CP

⇒ SP = ³⁵⁵/₁₀₀ × CP

⇒ 17785.5 = ^{355 CP}/₁₀₀

After cross multiplication

⇒ 17785.5 × 100 = 355 CP

⇒ 355 CP = 17785.5 × 100

⇒ CP = ^{17785.5 × 100}/₃₅₅

⇒ CP = ^1778550/₃₅₅ = 5010

⇒ CP = $5010 Answer

Similar Questions

(1) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

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

(3) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(4) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(5) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

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

(7) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

(8) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(9) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(10) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?