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) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

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

(4) William loses 71% by selling an article for $988.90. For how much should he sell it to get a profit of 70%?

(5) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(6) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

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

(8) If a trader gets a loss of 24% by selling 500 shares for $3503.60 then find the cost price of those shares.

(9) If a dealer gets a loss of 75% by selling 200 boxes of apple for $3702.50 then find the cost price.

(10) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price