Profit And Loss
Math MCQs

Question :    Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

Correct Answer  7110

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) = $32706

And, the profit = 360%

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 + 360} × 32706

= ^{100 × 32706}/₄₆₀

= ^3270600/₄₆₀ = 7110

Thus, the Cost Price (CP) = $7110 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 = 360%

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

= 360% of m

= 360% × m

= ³⁶⁰/₁₀₀ × m

⇒ Profit = ^{360 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 32706 = m + ^{360 m}/₁₀₀

⇒ 32706 = ^{100 m + 360 m}/₁₀₀

⇒ 32706 = ^{460 m}/₁₀₀

After cross multiplication, we get

32706 × 100 = 460 m

⇒ 460 m = 32706 × 100

⇒ m = ^{32706 × 100}/₄₆₀

⇒ m = ^3270600/₄₆₀ = 7110

⇒ m = 7110

Thus, the Cost Price (CP) = $7110 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) = $32706

And, the profit = 360%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 360% of 100 = 360

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

⇒ Sale Price (SP) = 100 + 360

⇒ Sale Price (SP) = 460

∵ If the Sale Price (SP) is 460, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₆₀

∴ If the Sale Price (SP) is 32706, then the Cost Price (CP)

= ¹⁰⁰/₄₆₀ × 32706

= ^{100 × 32706}/₄₆₀

= ^3270600/₄₆₀ = 7110

Thus, the Cost Price (CP) = $7110 Answer

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

Given, the sale price (SP) = $32706

And, the profit = 360%

Then, the Cost Price (CP) = ?

SP = 460% of CP

⇒ SP = ⁴⁶⁰/₁₀₀ × CP

⇒ 32706 = ^{460 CP}/₁₀₀

After cross multiplication

⇒ 32706 × 100 = 460 CP

⇒ 460 CP = 32706 × 100

⇒ CP = ^{32706 × 100}/₄₆₀

⇒ CP = ^3270600/₄₆₀ = 7110

⇒ CP = $7110 Answer

Similar Questions

(1) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(2) Mr. James loses 24% after selling an article for $805.60. For how much should he sell it to get a profit of 23%?

(3) 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%?

(4) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(5) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

(6) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(7) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?

(8) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?

(9) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(10) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.