Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

Correct Answer  7710

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) = $37779

And, the profit = 390%

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 + 390} × 37779

= ^{100 × 37779}/₄₉₀

= ^3777900/₄₉₀ = 7710

Thus, the Cost Price (CP) = $7710 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 = 390%

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

= 390% of m

= 390% × m

= ³⁹⁰/₁₀₀ × m

⇒ Profit = ^{390 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 37779 = m + ^{390 m}/₁₀₀

⇒ 37779 = ^{100 m + 390 m}/₁₀₀

⇒ 37779 = ^{490 m}/₁₀₀

After cross multiplication, we get

37779 × 100 = 490 m

⇒ 490 m = 37779 × 100

⇒ m = ^{37779 × 100}/₄₉₀

⇒ m = ^3777900/₄₉₀ = 7710

⇒ m = 7710

Thus, the Cost Price (CP) = $7710 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) = $37779

And, the profit = 390%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 390% of 100 = 390

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

⇒ Sale Price (SP) = 100 + 390

⇒ Sale Price (SP) = 490

∵ If the Sale Price (SP) is 490, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₉₀

∴ If the Sale Price (SP) is 37779, then the Cost Price (CP)

= ¹⁰⁰/₄₉₀ × 37779

= ^{100 × 37779}/₄₉₀

= ^3777900/₄₉₀ = 7710

Thus, the Cost Price (CP) = $7710 Answer

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

Given, the sale price (SP) = $37779

And, the profit = 390%

Then, the Cost Price (CP) = ?

SP = 490% of CP

⇒ SP = ⁴⁹⁰/₁₀₀ × CP

⇒ 37779 = ^{490 CP}/₁₀₀

After cross multiplication

⇒ 37779 × 100 = 490 CP

⇒ 490 CP = 37779 × 100

⇒ CP = ^{37779 × 100}/₄₉₀

⇒ CP = ^3777900/₄₉₀ = 7710

⇒ CP = $7710 Answer

Similar Questions

(1) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(2) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(3) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?

(4) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(5) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(6) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30

(7) If a trader gets a loss of 66% by selling ten TV sets for $4423.40 then find the cost price of all those TV sets

(8) Mr. Oliver loses 81% by selling an article for $742.90. For how much should he sell it to get a profit of 80%?

(9) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

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