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

(1) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?

(2) A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?

(3) Mr. Joseph loses 5% by selling an article for $104.50. For how much should he sell it to get a profit of 4%?

(4) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

(5) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(6) Find the cost price, if a dealer earns a profit of 305% by selling a plot for $24340.50

(7) A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.

(8) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(9) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?

(10) Find the cost price, if a trader gets a loss of 1% by selling an article for $9.9