Profit And Loss
Math MCQs

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

Correct Answer  910

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) = $1365

And, the profit = 50%

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 + 50} × 1365

= ^{100 × 1365}/₁₅₀

= ¹³⁶⁵⁰⁰/₁₅₀ = 910

Thus, the Cost Price (CP) = $910 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 = 50%

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

= 50% of m

= 50% × m

= ⁵⁰/₁₀₀ × m

⇒ Profit = ^{50 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1365 = m + ^{50 m}/₁₀₀

⇒ 1365 = ^{100 m + 50 m}/₁₀₀

⇒ 1365 = ^{150 m}/₁₀₀

After cross multiplication, we get

1365 × 100 = 150 m

⇒ 150 m = 1365 × 100

⇒ m = ^{1365 × 100}/₁₅₀

⇒ m = ¹³⁶⁵⁰⁰/₁₅₀ = 910

⇒ m = 910

Thus, the Cost Price (CP) = $910 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) = $1365

And, the profit = 50%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 50% of 100 = 50

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

⇒ Sale Price (SP) = 100 + 50

⇒ Sale Price (SP) = 150

∵ If the Sale Price (SP) is 150, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₅₀

∴ If the Sale Price (SP) is 1365, then the Cost Price (CP)

= ¹⁰⁰/₁₅₀ × 1365

= ^{100 × 1365}/₁₅₀

= ¹³⁶⁵⁰⁰/₁₅₀ = 910

Thus, the Cost Price (CP) = $910 Answer

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

Given, the sale price (SP) = $1365

And, the profit = 50%

Then, the Cost Price (CP) = ?

SP = 150% of CP

⇒ SP = ¹⁵⁰/₁₀₀ × CP

⇒ 1365 = ^{150 CP}/₁₀₀

After cross multiplication

⇒ 1365 × 100 = 150 CP

⇒ 150 CP = 1365 × 100

⇒ CP = ^{1365 × 100}/₁₅₀

⇒ CP = ¹³⁶⁵⁰⁰/₁₅₀ = 910

⇒ CP = $910 Answer

Similar Questions

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(2) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(3) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?

(4) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

(5) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(6) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

(7) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?

(8) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(9) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(10) A trader earns a profit of 170% by selling an article for $8937. Find the cost price.