Profit And Loss
Math MCQs

Question :    Find the cost price, if a broker earns a profit of 385% by selling an article for $36908.5

Correct Answer  7610

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) = $36908.5

And, the profit = 385%

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 + 385} × 36908.5

= ^{100 × 36908.5}/₄₈₅

= ^3690850/₄₈₅ = 7610

Thus, the Cost Price (CP) = $7610 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 = 385%

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

= 385% of m

= 385% × m

= ³⁸⁵/₁₀₀ × m

⇒ Profit = ^{385 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 36908.5 = m + ^{385 m}/₁₀₀

⇒ 36908.5 = ^{100 m + 385 m}/₁₀₀

⇒ 36908.5 = ^{485 m}/₁₀₀

After cross multiplication, we get

36908.5 × 100 = 485 m

⇒ 485 m = 36908.5 × 100

⇒ m = ^{36908.5 × 100}/₄₈₅

⇒ m = ^3690850/₄₈₅ = 7610

⇒ m = 7610

Thus, the Cost Price (CP) = $7610 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) = $36908.5

And, the profit = 385%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 385% of 100 = 385

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

⇒ Sale Price (SP) = 100 + 385

⇒ Sale Price (SP) = 485

∵ If the Sale Price (SP) is 485, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₈₅

∴ If the Sale Price (SP) is 36908.5, then the Cost Price (CP)

= ¹⁰⁰/₄₈₅ × 36908.5

= ^{100 × 36908.5}/₄₈₅

= ^3690850/₄₈₅ = 7610

Thus, the Cost Price (CP) = $7610 Answer

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

Given, the sale price (SP) = $36908.5

And, the profit = 385%

Then, the Cost Price (CP) = ?

SP = 485% of CP

⇒ SP = ⁴⁸⁵/₁₀₀ × CP

⇒ 36908.5 = ^{485 CP}/₁₀₀

After cross multiplication

⇒ 36908.5 × 100 = 485 CP

⇒ 485 CP = 36908.5 × 100

⇒ CP = ^{36908.5 × 100}/₄₈₅

⇒ CP = ^3690850/₄₈₅ = 7610

⇒ CP = $7610 Answer

Similar Questions

(1) Noah loses 76% by selling an article for $878.40. For how much should he sell it to get a profit of 75%?

(2) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

(3) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.

(4) Mr. Jack gets a profit of 195% by selling some articles for $11239.50. What was his cost price?

(5) Mr. Donald loses 84% by selling an article for $649.60. For how much should he sell it to get a profit of 83%?

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

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

(8) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.

(9) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

(10) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.