Profit And Loss
Math MCQs

Question :    After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

Correct Answer  5710

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) = $22269

And, the profit = 290%

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 + 290} × 22269

= ^{100 × 22269}/₃₉₀

= ^2226900/₃₉₀ = 5710

Thus, the Cost Price (CP) = $5710 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 = 290%

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

= 290% of m

= 290% × m

= ²⁹⁰/₁₀₀ × m

⇒ Profit = ^{290 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 22269 = m + ^{290 m}/₁₀₀

⇒ 22269 = ^{100 m + 290 m}/₁₀₀

⇒ 22269 = ^{390 m}/₁₀₀

After cross multiplication, we get

22269 × 100 = 390 m

⇒ 390 m = 22269 × 100

⇒ m = ^{22269 × 100}/₃₉₀

⇒ m = ^2226900/₃₉₀ = 5710

⇒ m = 5710

Thus, the Cost Price (CP) = $5710 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) = $22269

And, the profit = 290%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 290% of 100 = 290

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

⇒ Sale Price (SP) = 100 + 290

⇒ Sale Price (SP) = 390

∵ If the Sale Price (SP) is 390, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₉₀

∴ If the Sale Price (SP) is 22269, then the Cost Price (CP)

= ¹⁰⁰/₃₉₀ × 22269

= ^{100 × 22269}/₃₉₀

= ^2226900/₃₉₀ = 5710

Thus, the Cost Price (CP) = $5710 Answer

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

Given, the sale price (SP) = $22269

And, the profit = 290%

Then, the Cost Price (CP) = ?

SP = 390% of CP

⇒ SP = ³⁹⁰/₁₀₀ × CP

⇒ 22269 = ^{390 CP}/₁₀₀

After cross multiplication

⇒ 22269 × 100 = 390 CP

⇒ 390 CP = 22269 × 100

⇒ CP = ^{22269 × 100}/₃₉₀

⇒ CP = ^2226900/₃₉₀ = 5710

⇒ CP = $5710 Answer

Similar Questions

(1) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

(2) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

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

(4) 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.

(5) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(6) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

(7) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90

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

(9) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

(10) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?