Profit And Loss
Math MCQs

Question :    A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?

Correct Answer  1810

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) = $3529.5

And, the profit = 95%

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 + 95} × 3529.5

= ^{100 × 3529.5}/₁₉₅

= ³⁵²⁹⁵⁰/₁₉₅ = 1810

Thus, the Cost Price (CP) = $1810 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 = 95%

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

= 95% of m

= 95% × m

= ⁹⁵/₁₀₀ × m

⇒ Profit = ^{95 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 3529.5 = m + ^{95 m}/₁₀₀

⇒ 3529.5 = ^{100 m + 95 m}/₁₀₀

⇒ 3529.5 = ^{195 m}/₁₀₀

After cross multiplication, we get

3529.5 × 100 = 195 m

⇒ 195 m = 3529.5 × 100

⇒ m = ^{3529.5 × 100}/₁₉₅

⇒ m = ³⁵²⁹⁵⁰/₁₉₅ = 1810

⇒ m = 1810

Thus, the Cost Price (CP) = $1810 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) = $3529.5

And, the profit = 95%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 95% of 100 = 95

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

⇒ Sale Price (SP) = 100 + 95

⇒ Sale Price (SP) = 195

∵ If the Sale Price (SP) is 195, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₉₅

∴ If the Sale Price (SP) is 3529.5, then the Cost Price (CP)

= ¹⁰⁰/₁₉₅ × 3529.5

= ^{100 × 3529.5}/₁₉₅

= ³⁵²⁹⁵⁰/₁₉₅ = 1810

Thus, the Cost Price (CP) = $1810 Answer

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

Given, the sale price (SP) = $3529.5

And, the profit = 95%

Then, the Cost Price (CP) = ?

SP = 195% of CP

⇒ SP = ¹⁹⁵/₁₀₀ × CP

⇒ 3529.5 = ^{195 CP}/₁₀₀

After cross multiplication

⇒ 3529.5 × 100 = 195 CP

⇒ 195 CP = 3529.5 × 100

⇒ CP = ^{3529.5 × 100}/₁₉₅

⇒ CP = ³⁵²⁹⁵⁰/₁₉₅ = 1810

⇒ CP = $1810 Answer

Similar Questions

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

(3) If a broker loses 39% by selling some of his stocks for $1104.10 then he should sell them for how much to get a profit of 38%?

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(8) If a vendor buys 60 articles for $1 and sells 59 articles for $1 then, calculate the profit in percent.

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(10) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?