Profit And Loss
Math MCQs

Question :    A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

Correct Answer  6110

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) = $25051

And, the profit = 310%

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 + 310} × 25051

= ^{100 × 25051}/₄₁₀

= ^2505100/₄₁₀ = 6110

Thus, the Cost Price (CP) = $6110 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 = 310%

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

= 310% of m

= 310% × m

= ³¹⁰/₁₀₀ × m

⇒ Profit = ^{310 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 25051 = m + ^{310 m}/₁₀₀

⇒ 25051 = ^{100 m + 310 m}/₁₀₀

⇒ 25051 = ^{410 m}/₁₀₀

After cross multiplication, we get

25051 × 100 = 410 m

⇒ 410 m = 25051 × 100

⇒ m = ^{25051 × 100}/₄₁₀

⇒ m = ^2505100/₄₁₀ = 6110

⇒ m = 6110

Thus, the Cost Price (CP) = $6110 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) = $25051

And, the profit = 310%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 310% of 100 = 310

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

⇒ Sale Price (SP) = 100 + 310

⇒ Sale Price (SP) = 410

∵ If the Sale Price (SP) is 410, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₁₀

∴ If the Sale Price (SP) is 25051, then the Cost Price (CP)

= ¹⁰⁰/₄₁₀ × 25051

= ^{100 × 25051}/₄₁₀

= ^2505100/₄₁₀ = 6110

Thus, the Cost Price (CP) = $6110 Answer

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

Given, the sale price (SP) = $25051

And, the profit = 310%

Then, the Cost Price (CP) = ?

SP = 410% of CP

⇒ SP = ⁴¹⁰/₁₀₀ × CP

⇒ 25051 = ^{410 CP}/₁₀₀

After cross multiplication

⇒ 25051 × 100 = 410 CP

⇒ 410 CP = 25051 × 100

⇒ CP = ^{25051 × 100}/₄₁₀

⇒ CP = ^2505100/₄₁₀ = 6110

⇒ CP = $6110 Answer

Similar Questions

(1) Peter loses 3% by selling an article for $9.70. For how much should he sell it to get a profit of 2%?

(2) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(3) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?

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

(5) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

(6) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70

(7) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90

(8) Find the cost price, if a share broker gets a loss of 26% by selling 100 shares for $3707.40.

(9) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(10) Mrs. Julie buys 16 oranges for $1 and sells 15 oranges for $1. What is her profit percent in this sale?