Profit And Loss
Math MCQs

Question :    Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

Correct Answer  7510

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) = $36048

And, the profit = 380%

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 + 380} × 36048

= ^{100 × 36048}/₄₈₀

= ^3604800/₄₈₀ = 7510

Thus, the Cost Price (CP) = $7510 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 = 380%

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

= 380% of m

= 380% × m

= ³⁸⁰/₁₀₀ × m

⇒ Profit = ^{380 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 36048 = m + ^{380 m}/₁₀₀

⇒ 36048 = ^{100 m + 380 m}/₁₀₀

⇒ 36048 = ^{480 m}/₁₀₀

After cross multiplication, we get

36048 × 100 = 480 m

⇒ 480 m = 36048 × 100

⇒ m = ^{36048 × 100}/₄₈₀

⇒ m = ^3604800/₄₈₀ = 7510

⇒ m = 7510

Thus, the Cost Price (CP) = $7510 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) = $36048

And, the profit = 380%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 380% of 100 = 380

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

⇒ Sale Price (SP) = 100 + 380

⇒ Sale Price (SP) = 480

∵ If the Sale Price (SP) is 480, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₈₀

∴ If the Sale Price (SP) is 36048, then the Cost Price (CP)

= ¹⁰⁰/₄₈₀ × 36048

= ^{100 × 36048}/₄₈₀

= ^3604800/₄₈₀ = 7510

Thus, the Cost Price (CP) = $7510 Answer

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

Given, the sale price (SP) = $36048

And, the profit = 380%

Then, the Cost Price (CP) = ?

SP = 480% of CP

⇒ SP = ⁴⁸⁰/₁₀₀ × CP

⇒ 36048 = ^{480 CP}/₁₀₀

After cross multiplication

⇒ 36048 × 100 = 480 CP

⇒ 480 CP = 36048 × 100

⇒ CP = ^{36048 × 100}/₄₈₀

⇒ CP = ^3604800/₄₈₀ = 7510

⇒ CP = $7510 Answer

Similar Questions

(1) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718

(2) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

(3) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(4) Find the cost price, if a trader gets a loss of 1% by selling an article for $9.9

(5) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

(6) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.

(7) Find the cost price, if a trader earns a profit of 395% by selling an article for $38659.5

(8) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

(9) A trader loses 55% by selling an article for $1174.50. For how much should he sell it to get a profit of 54%?

(10) William loses 33% by selling an article for $1011.70. For how much should he sell it to get a profit of 32%?