Profit And Loss
MCQs Math


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


Correct Answer  3910

Solution And 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) = $11730

And, the profit = 200%

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 + 200 × 11730

= 100 × 11730/300

= 1173000/300 = 3910

Thus, the Cost Price (CP) = $3910 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 = 200%

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

= 200% of m

= 200% × m

= 200/100 × m

⇒ Profit = 200 m/100

Calculation of Cost Price (CP)

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

⇒ 11730 = m + 200 m/100

⇒ 11730 = 100 m + 200 m/100

⇒ 11730 = 300 m/100

After cross multiplication, we get

11730 × 100 = 300 m

⇒ 300 m = 11730 × 100

⇒ m = 11730 × 100/300

⇒ m = 1173000/300 = 3910

⇒ m = 3910

Thus, the Cost Price (CP) = $3910 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) = $11730

And, the profit = 200%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 200% of 100 = 200

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

⇒ Sale Price (SP) = 100 + 200

⇒ Sale Price (SP) = 300

∵ If the Sale Price (SP) is 300, then the Cost Price (CP) = 100

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

= 100/300

∴ If the Sale Price (SP) is 11730, then the Cost Price (CP)

= 100/300 × 11730

= 100 × 11730/300

= 1173000/300 = 3910

Thus, the Cost Price (CP) = $3910 Answer

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

Given, the sale price (SP) = $11730

And, the profit = 200%

Then, the Cost Price (CP) = ?

SP = 300% of CP

⇒ SP = 300/100 × CP

⇒ 11730 = 300 CP/100

After cross multiplication

⇒ 11730 × 100 = 300 CP

⇒ 300 CP = 11730 × 100

⇒ CP = 11730 × 100/300

⇒ CP = 1173000/300 = 3910

⇒ CP = $3910 Answer


Similar Questions

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(2) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

(3) Find the cost price, if Mrs. Olivia earns a profit of 160% by selling some articles for $8086

(4) 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?

(5) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(6) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

(7) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

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

(9) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?

(10) Find the cost price, if a trader gets a loss of 19% by selling an article for $2924.10


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