Profit And Loss
Math MCQs

Question :    Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640

Correct Answer  5910

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) = $23640

And, the profit = 300%

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 + 300} × 23640

= ^{100 × 23640}/₄₀₀

= ^2364000/₄₀₀ = 5910

Thus, the Cost Price (CP) = $5910 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 = 300%

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

= 300% of m

= 300% × m

= ³⁰⁰/₁₀₀ × m

⇒ Profit = ^{300 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 23640 = m + ^{300 m}/₁₀₀

⇒ 23640 = ^{100 m + 300 m}/₁₀₀

⇒ 23640 = ^{400 m}/₁₀₀

After cross multiplication, we get

23640 × 100 = 400 m

⇒ 400 m = 23640 × 100

⇒ m = ^{23640 × 100}/₄₀₀

⇒ m = ^2364000/₄₀₀ = 5910

⇒ m = 5910

Thus, the Cost Price (CP) = $5910 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) = $23640

And, the profit = 300%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 300% of 100 = 300

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

⇒ Sale Price (SP) = 100 + 300

⇒ Sale Price (SP) = 400

∵ If the Sale Price (SP) is 400, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₄₀₀

∴ If the Sale Price (SP) is 23640, then the Cost Price (CP)

= ¹⁰⁰/₄₀₀ × 23640

= ^{100 × 23640}/₄₀₀

= ^2364000/₄₀₀ = 5910

Thus, the Cost Price (CP) = $5910 Answer

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

Given, the sale price (SP) = $23640

And, the profit = 300%

Then, the Cost Price (CP) = ?

SP = 400% of CP

⇒ SP = ⁴⁰⁰/₁₀₀ × CP

⇒ 23640 = ^{400 CP}/₁₀₀

After cross multiplication

⇒ 23640 × 100 = 400 CP

⇒ 400 CP = 23640 × 100

⇒ CP = ^{23640 × 100}/₄₀₀

⇒ CP = ^2364000/₄₀₀ = 5910

⇒ CP = $5910 Answer

Similar Questions

(1) By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.

(2) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(3) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80

(4) What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

(5) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.

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

(7) To earn a profit of 7% Mr. Robert should sell his article for how much if he gets a loss of 8% by selling it for $239.20?

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

(9) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(10) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?