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

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(2) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(3) Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.

(4) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(5) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

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

(7) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(8) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

(9) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?

(10) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.