Profit And Loss
Math MCQs

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

Correct Answer  3710

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) = $10759

And, the profit = 190%

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 + 190} × 10759

= ^{100 × 10759}/₂₉₀

= ^1075900/₂₉₀ = 3710

Thus, the Cost Price (CP) = $3710 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 = 190%

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

= 190% of m

= 190% × m

= ¹⁹⁰/₁₀₀ × m

⇒ Profit = ^{190 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 10759 = m + ^{190 m}/₁₀₀

⇒ 10759 = ^{100 m + 190 m}/₁₀₀

⇒ 10759 = ^{290 m}/₁₀₀

After cross multiplication, we get

10759 × 100 = 290 m

⇒ 290 m = 10759 × 100

⇒ m = ^{10759 × 100}/₂₉₀

⇒ m = ^1075900/₂₉₀ = 3710

⇒ m = 3710

Thus, the Cost Price (CP) = $3710 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) = $10759

And, the profit = 190%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 190% of 100 = 190

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

⇒ Sale Price (SP) = 100 + 190

⇒ Sale Price (SP) = 290

∵ If the Sale Price (SP) is 290, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₉₀

∴ If the Sale Price (SP) is 10759, then the Cost Price (CP)

= ¹⁰⁰/₂₉₀ × 10759

= ^{100 × 10759}/₂₉₀

= ^1075900/₂₉₀ = 3710

Thus, the Cost Price (CP) = $3710 Answer

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

Given, the sale price (SP) = $10759

And, the profit = 190%

Then, the Cost Price (CP) = ?

SP = 290% of CP

⇒ SP = ²⁹⁰/₁₀₀ × CP

⇒ 10759 = ^{290 CP}/₁₀₀

After cross multiplication

⇒ 10759 × 100 = 290 CP

⇒ 290 CP = 10759 × 100

⇒ CP = ^{10759 × 100}/₂₉₀

⇒ CP = ^1075900/₂₉₀ = 3710

⇒ CP = $3710 Answer

Similar Questions

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

(2) Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

(3) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(4) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?

(5) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

(6) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(7) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.

(8) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(9) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

(10) Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?