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

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(2) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

(3) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(4) Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

(5) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

(6) By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

(7) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?

(8) Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640

(9) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?

(10) Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%