Profit And Loss
Math MCQs

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

Correct Answer  710

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) = $994

And, the profit = 40%

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 + 40} × 994

= ^{100 × 994}/₁₄₀

= ⁹⁹⁴⁰⁰/₁₄₀ = 710

Thus, the Cost Price (CP) = $710 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 = 40%

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

= 40% of m

= 40% × m

= ⁴⁰/₁₀₀ × m

⇒ Profit = ^{40 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 994 = m + ^{40 m}/₁₀₀

⇒ 994 = ^{100 m + 40 m}/₁₀₀

⇒ 994 = ^{140 m}/₁₀₀

After cross multiplication, we get

994 × 100 = 140 m

⇒ 140 m = 994 × 100

⇒ m = ^{994 × 100}/₁₄₀

⇒ m = ⁹⁹⁴⁰⁰/₁₄₀ = 710

⇒ m = 710

Thus, the Cost Price (CP) = $710 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) = $994

And, the profit = 40%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 40% of 100 = 40

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

⇒ Sale Price (SP) = 100 + 40

⇒ Sale Price (SP) = 140

∵ If the Sale Price (SP) is 140, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₄₀

∴ If the Sale Price (SP) is 994, then the Cost Price (CP)

= ¹⁰⁰/₁₄₀ × 994

= ^{100 × 994}/₁₄₀

= ⁹⁹⁴⁰⁰/₁₄₀ = 710

Thus, the Cost Price (CP) = $710 Answer

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

Given, the sale price (SP) = $994

And, the profit = 40%

Then, the Cost Price (CP) = ?

SP = 140% of CP

⇒ SP = ¹⁴⁰/₁₀₀ × CP

⇒ 994 = ^{140 CP}/₁₀₀

After cross multiplication

⇒ 994 × 100 = 140 CP

⇒ 140 CP = 994 × 100

⇒ CP = ^{994 × 100}/₁₄₀

⇒ CP = ⁹⁹⁴⁰⁰/₁₄₀ = 710

⇒ CP = $710 Answer

Similar Questions

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(2) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(3) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

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

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