Profit And Loss
Math MCQs

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

Correct Answer  5810

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) = $22949.5

And, the profit = 295%

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 + 295} × 22949.5

= ^{100 × 22949.5}/₃₉₅

= ^2294950/₃₉₅ = 5810

Thus, the Cost Price (CP) = $5810 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 = 295%

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

= 295% of m

= 295% × m

= ²⁹⁵/₁₀₀ × m

⇒ Profit = ^{295 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 22949.5 = m + ^{295 m}/₁₀₀

⇒ 22949.5 = ^{100 m + 295 m}/₁₀₀

⇒ 22949.5 = ^{395 m}/₁₀₀

After cross multiplication, we get

22949.5 × 100 = 395 m

⇒ 395 m = 22949.5 × 100

⇒ m = ^{22949.5 × 100}/₃₉₅

⇒ m = ^2294950/₃₉₅ = 5810

⇒ m = 5810

Thus, the Cost Price (CP) = $5810 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) = $22949.5

And, the profit = 295%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 295% of 100 = 295

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

⇒ Sale Price (SP) = 100 + 295

⇒ Sale Price (SP) = 395

∵ If the Sale Price (SP) is 395, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₉₅

∴ If the Sale Price (SP) is 22949.5, then the Cost Price (CP)

= ¹⁰⁰/₃₉₅ × 22949.5

= ^{100 × 22949.5}/₃₉₅

= ^2294950/₃₉₅ = 5810

Thus, the Cost Price (CP) = $5810 Answer

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

Given, the sale price (SP) = $22949.5

And, the profit = 295%

Then, the Cost Price (CP) = ?

SP = 395% of CP

⇒ SP = ³⁹⁵/₁₀₀ × CP

⇒ 22949.5 = ^{395 CP}/₁₀₀

After cross multiplication

⇒ 22949.5 × 100 = 395 CP

⇒ 395 CP = 22949.5 × 100

⇒ CP = ^{22949.5 × 100}/₃₉₅

⇒ CP = ^2294950/₃₉₅ = 5810

⇒ CP = $5810 Answer

Similar Questions

(1) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(2) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

(3) The cost price of an article is $15 and the sale price is $20, then find the profit and profit percent.

(4) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?

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

(6) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

(7) Find the cost price, if a trader gets a loss of 74% by selling 50 bags of rice for $3798.60

(8) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.

(9) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(10) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.