Profit And Loss
Math MCQs

Question :    Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

Correct Answer  2310

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) = $5082

And, the profit = 120%

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 + 120} × 5082

= ^{100 × 5082}/₂₂₀

= ⁵⁰⁸²⁰⁰/₂₂₀ = 2310

Thus, the Cost Price (CP) = $2310 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 = 120%

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

= 120% of m

= 120% × m

= ¹²⁰/₁₀₀ × m

⇒ Profit = ^{120 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 5082 = m + ^{120 m}/₁₀₀

⇒ 5082 = ^{100 m + 120 m}/₁₀₀

⇒ 5082 = ^{220 m}/₁₀₀

After cross multiplication, we get

5082 × 100 = 220 m

⇒ 220 m = 5082 × 100

⇒ m = ^{5082 × 100}/₂₂₀

⇒ m = ⁵⁰⁸²⁰⁰/₂₂₀ = 2310

⇒ m = 2310

Thus, the Cost Price (CP) = $2310 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) = $5082

And, the profit = 120%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 120% of 100 = 120

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

⇒ Sale Price (SP) = 100 + 120

⇒ Sale Price (SP) = 220

∵ If the Sale Price (SP) is 220, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₂₀

∴ If the Sale Price (SP) is 5082, then the Cost Price (CP)

= ¹⁰⁰/₂₂₀ × 5082

= ^{100 × 5082}/₂₂₀

= ⁵⁰⁸²⁰⁰/₂₂₀ = 2310

Thus, the Cost Price (CP) = $2310 Answer

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

Given, the sale price (SP) = $5082

And, the profit = 120%

Then, the Cost Price (CP) = ?

SP = 220% of CP

⇒ SP = ²²⁰/₁₀₀ × CP

⇒ 5082 = ^{220 CP}/₁₀₀

After cross multiplication

⇒ 5082 × 100 = 220 CP

⇒ 220 CP = 5082 × 100

⇒ CP = ^{5082 × 100}/₂₂₀

⇒ CP = ⁵⁰⁸²⁰⁰/₂₂₀ = 2310

⇒ CP = $2310 Answer

Similar Questions

(1) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(2) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(3) If a shopkeeper loses 38% by selling some articles for $1091.20 then, he should sell them to get a profit of 37% for how much?

(4) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(5) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?

(6) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(7) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(8) What will be the cost price if Peter eans a profit of 15% by selling a scooty for $241.5?

(9) Find the cost price if a broker earned 375% while dealing a house for $35197.50

(10) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.