Profit And Loss
Math MCQs

Question :    Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.

Correct Answer  3510

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) = $9828

And, the profit = 180%

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 + 180} × 9828

= ^{100 × 9828}/₂₈₀

= ⁹⁸²⁸⁰⁰/₂₈₀ = 3510

Thus, the Cost Price (CP) = $3510 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 = 180%

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

= 180% of m

= 180% × m

= ¹⁸⁰/₁₀₀ × m

⇒ Profit = ^{180 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 9828 = m + ^{180 m}/₁₀₀

⇒ 9828 = ^{100 m + 180 m}/₁₀₀

⇒ 9828 = ^{280 m}/₁₀₀

After cross multiplication, we get

9828 × 100 = 280 m

⇒ 280 m = 9828 × 100

⇒ m = ^{9828 × 100}/₂₈₀

⇒ m = ⁹⁸²⁸⁰⁰/₂₈₀ = 3510

⇒ m = 3510

Thus, the Cost Price (CP) = $3510 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) = $9828

And, the profit = 180%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 180% of 100 = 180

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

⇒ Sale Price (SP) = 100 + 180

⇒ Sale Price (SP) = 280

∵ If the Sale Price (SP) is 280, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₈₀

∴ If the Sale Price (SP) is 9828, then the Cost Price (CP)

= ¹⁰⁰/₂₈₀ × 9828

= ^{100 × 9828}/₂₈₀

= ⁹⁸²⁸⁰⁰/₂₈₀ = 3510

Thus, the Cost Price (CP) = $3510 Answer

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

Given, the sale price (SP) = $9828

And, the profit = 180%

Then, the Cost Price (CP) = ?

SP = 280% of CP

⇒ SP = ²⁸⁰/₁₀₀ × CP

⇒ 9828 = ^{280 CP}/₁₀₀

After cross multiplication

⇒ 9828 × 100 = 280 CP

⇒ 280 CP = 9828 × 100

⇒ CP = ^{9828 × 100}/₂₈₀

⇒ CP = ⁹⁸²⁸⁰⁰/₂₈₀ = 3510

⇒ CP = $3510 Answer

Similar Questions

(1) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

(2) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

(3) For how much should a trader sell an item to get a profit of 49% if he loses 50% by selling it for $1180.00?

(4) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(5) After selling a furniture for $481.60 a shopkeeper gets a loss of 14%. In order to get a profit of 13% he should sell in for how much?

(6) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?

(7) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

(8) The cost price of an article is $15 and the sale price is $20, then find the profit and profit percent.

(9) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(10) A shopkeeper loses 51% by selling an article for $1180.90. For how much should he sell it to get a profit of 50%?