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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(3) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(4) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(5) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

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(7) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(8) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(9) Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.

(10) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5