Profit And Loss
Math MCQs

Question :    By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

Correct Answer  5510

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) = $20938

And, the profit = 280%

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 + 280} × 20938

= ^{100 × 20938}/₃₈₀

= ^2093800/₃₈₀ = 5510

Thus, the Cost Price (CP) = $5510 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 = 280%

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

= 280% of m

= 280% × m

= ²⁸⁰/₁₀₀ × m

⇒ Profit = ^{280 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 20938 = m + ^{280 m}/₁₀₀

⇒ 20938 = ^{100 m + 280 m}/₁₀₀

⇒ 20938 = ^{380 m}/₁₀₀

After cross multiplication, we get

20938 × 100 = 380 m

⇒ 380 m = 20938 × 100

⇒ m = ^{20938 × 100}/₃₈₀

⇒ m = ^2093800/₃₈₀ = 5510

⇒ m = 5510

Thus, the Cost Price (CP) = $5510 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) = $20938

And, the profit = 280%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 280% of 100 = 280

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

⇒ Sale Price (SP) = 100 + 280

⇒ Sale Price (SP) = 380

∵ If the Sale Price (SP) is 380, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₈₀

∴ If the Sale Price (SP) is 20938, then the Cost Price (CP)

= ¹⁰⁰/₃₈₀ × 20938

= ^{100 × 20938}/₃₈₀

= ^2093800/₃₈₀ = 5510

Thus, the Cost Price (CP) = $5510 Answer

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

Given, the sale price (SP) = $20938

And, the profit = 280%

Then, the Cost Price (CP) = ?

SP = 380% of CP

⇒ SP = ³⁸⁰/₁₀₀ × CP

⇒ 20938 = ^{380 CP}/₁₀₀

After cross multiplication

⇒ 20938 × 100 = 380 CP

⇒ 380 CP = 20938 × 100

⇒ CP = ^{20938 × 100}/₃₈₀

⇒ CP = ^2093800/₃₈₀ = 5510

⇒ CP = $5510 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

(2) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

(3) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

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

(5) Mr. Noah loses 37% by selling an article for $1077.30. For how much should he sell it to get a profit of 36%?

(6) If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

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

(8) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(9) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(10) Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5