Profit And Loss
Math MCQs

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

Correct Answer  7810

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) = $38659.5

And, the profit = 395%

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 + 395} × 38659.5

= ^{100 × 38659.5}/₄₉₅

= ^3865950/₄₉₅ = 7810

Thus, the Cost Price (CP) = $7810 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 = 395%

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

= 395% of m

= 395% × m

= ³⁹⁵/₁₀₀ × m

⇒ Profit = ^{395 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 38659.5 = m + ^{395 m}/₁₀₀

⇒ 38659.5 = ^{100 m + 395 m}/₁₀₀

⇒ 38659.5 = ^{495 m}/₁₀₀

After cross multiplication, we get

38659.5 × 100 = 495 m

⇒ 495 m = 38659.5 × 100

⇒ m = ^{38659.5 × 100}/₄₉₅

⇒ m = ^3865950/₄₉₅ = 7810

⇒ m = 7810

Thus, the Cost Price (CP) = $7810 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) = $38659.5

And, the profit = 395%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 395% of 100 = 395

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

⇒ Sale Price (SP) = 100 + 395

⇒ Sale Price (SP) = 495

∵ If the Sale Price (SP) is 495, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₉₅

∴ If the Sale Price (SP) is 38659.5, then the Cost Price (CP)

= ¹⁰⁰/₄₉₅ × 38659.5

= ^{100 × 38659.5}/₄₉₅

= ^3865950/₄₉₅ = 7810

Thus, the Cost Price (CP) = $7810 Answer

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

Given, the sale price (SP) = $38659.5

And, the profit = 395%

Then, the Cost Price (CP) = ?

SP = 495% of CP

⇒ SP = ⁴⁹⁵/₁₀₀ × CP

⇒ 38659.5 = ^{495 CP}/₁₀₀

After cross multiplication

⇒ 38659.5 × 100 = 495 CP

⇒ 495 CP = 38659.5 × 100

⇒ CP = ^{38659.5 × 100}/₄₉₅

⇒ CP = ^3865950/₄₉₅ = 7810

⇒ CP = $7810 Answer

Similar Questions

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(2) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(3) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?

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

(5) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?

(6) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(7) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

(8) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(9) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

(10) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.