Profit And Loss
Math MCQs

Question :    If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

Correct Answer  510

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) = $663

And, the profit = 30%

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 + 30} × 663

= ^{100 × 663}/₁₃₀

= ⁶⁶³⁰⁰/₁₃₀ = 510

Thus, the Cost Price (CP) = $510 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 = 30%

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

= 30% of m

= 30% × m

= ³⁰/₁₀₀ × m

⇒ Profit = ^{30 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 663 = m + ^{30 m}/₁₀₀

⇒ 663 = ^{100 m + 30 m}/₁₀₀

⇒ 663 = ^{130 m}/₁₀₀

After cross multiplication, we get

663 × 100 = 130 m

⇒ 130 m = 663 × 100

⇒ m = ^{663 × 100}/₁₃₀

⇒ m = ⁶⁶³⁰⁰/₁₃₀ = 510

⇒ m = 510

Thus, the Cost Price (CP) = $510 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) = $663

And, the profit = 30%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 30% of 100 = 30

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

⇒ Sale Price (SP) = 100 + 30

⇒ Sale Price (SP) = 130

∵ If the Sale Price (SP) is 130, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₃₀

∴ If the Sale Price (SP) is 663, then the Cost Price (CP)

= ¹⁰⁰/₁₃₀ × 663

= ^{100 × 663}/₁₃₀

= ⁶⁶³⁰⁰/₁₃₀ = 510

Thus, the Cost Price (CP) = $510 Answer

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

Given, the sale price (SP) = $663

And, the profit = 30%

Then, the Cost Price (CP) = ?

SP = 130% of CP

⇒ SP = ¹³⁰/₁₀₀ × CP

⇒ 663 = ^{130 CP}/₁₀₀

After cross multiplication

⇒ 663 × 100 = 130 CP

⇒ 130 CP = 663 × 100

⇒ CP = ^{663 × 100}/₁₃₀

⇒ CP = ⁶⁶³⁰⁰/₁₃₀ = 510

⇒ CP = $510 Answer

Similar Questions

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(2) Find the cost price, if a trader gets a loss of 69% by selling 12 bags of fruit for $4219.10

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(4) 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%?

(5) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(6) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

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(8) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.

(9) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(10) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5