Profit And Loss
Math MCQs

Question :    Find the cost price, if a dealer earns a profit of 345% by selling some goods for $30304.5

Correct Answer  6810

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) = $30304.5

And, the profit = 345%

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 + 345} × 30304.5

= ^{100 × 30304.5}/₄₄₅

= ^3030450/₄₄₅ = 6810

Thus, the Cost Price (CP) = $6810 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 = 345%

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

= 345% of m

= 345% × m

= ³⁴⁵/₁₀₀ × m

⇒ Profit = ^{345 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 30304.5 = m + ^{345 m}/₁₀₀

⇒ 30304.5 = ^{100 m + 345 m}/₁₀₀

⇒ 30304.5 = ^{445 m}/₁₀₀

After cross multiplication, we get

30304.5 × 100 = 445 m

⇒ 445 m = 30304.5 × 100

⇒ m = ^{30304.5 × 100}/₄₄₅

⇒ m = ^3030450/₄₄₅ = 6810

⇒ m = 6810

Thus, the Cost Price (CP) = $6810 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) = $30304.5

And, the profit = 345%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 345% of 100 = 345

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

⇒ Sale Price (SP) = 100 + 345

⇒ Sale Price (SP) = 445

∵ If the Sale Price (SP) is 445, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₄₅

∴ If the Sale Price (SP) is 30304.5, then the Cost Price (CP)

= ¹⁰⁰/₄₄₅ × 30304.5

= ^{100 × 30304.5}/₄₄₅

= ^3030450/₄₄₅ = 6810

Thus, the Cost Price (CP) = $6810 Answer

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

Given, the sale price (SP) = $30304.5

And, the profit = 345%

Then, the Cost Price (CP) = ?

SP = 445% of CP

⇒ SP = ⁴⁴⁵/₁₀₀ × CP

⇒ 30304.5 = ^{445 CP}/₁₀₀

After cross multiplication

⇒ 30304.5 × 100 = 445 CP

⇒ 445 CP = 30304.5 × 100

⇒ CP = ^{30304.5 × 100}/₄₄₅

⇒ CP = ^3030450/₄₄₅ = 6810

⇒ CP = $6810 Answer

Similar Questions

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(2) Mr. William buys 15 toffees for $1 and sells 14 tofees for $1. What is the profit percent?

(3) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.

(4) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70

(5) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90

(6) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

(7) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(8) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(9) In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.

(10) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?