Profit And Loss
Math MCQs

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

Correct Answer  6910

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) = $31095

And, the profit = 350%

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 + 350} × 31095

= ^{100 × 31095}/₄₅₀

= ^3109500/₄₅₀ = 6910

Thus, the Cost Price (CP) = $6910 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 = 350%

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

= 350% of m

= 350% × m

= ³⁵⁰/₁₀₀ × m

⇒ Profit = ^{350 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 31095 = m + ^{350 m}/₁₀₀

⇒ 31095 = ^{100 m + 350 m}/₁₀₀

⇒ 31095 = ^{450 m}/₁₀₀

After cross multiplication, we get

31095 × 100 = 450 m

⇒ 450 m = 31095 × 100

⇒ m = ^{31095 × 100}/₄₅₀

⇒ m = ^3109500/₄₅₀ = 6910

⇒ m = 6910

Thus, the Cost Price (CP) = $6910 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) = $31095

And, the profit = 350%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 350% of 100 = 350

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

⇒ Sale Price (SP) = 100 + 350

⇒ Sale Price (SP) = 450

∵ If the Sale Price (SP) is 450, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₅₀

∴ If the Sale Price (SP) is 31095, then the Cost Price (CP)

= ¹⁰⁰/₄₅₀ × 31095

= ^{100 × 31095}/₄₅₀

= ^3109500/₄₅₀ = 6910

Thus, the Cost Price (CP) = $6910 Answer

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

Given, the sale price (SP) = $31095

And, the profit = 350%

Then, the Cost Price (CP) = ?

SP = 450% of CP

⇒ SP = ⁴⁵⁰/₁₀₀ × CP

⇒ 31095 = ^{450 CP}/₁₀₀

After cross multiplication

⇒ 31095 × 100 = 450 CP

⇒ 450 CP = 31095 × 100

⇒ CP = ^{31095 × 100}/₄₅₀

⇒ CP = ^3109500/₄₅₀ = 6910

⇒ CP = $6910 Answer

Similar Questions

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(2) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.

(3) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(4) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.

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

(7) If a hawker bought 22 apples per $1 and sold them at a rate of 21 apples per $1, then what would his profit percent be?

(8) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70

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

(10) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?