Profit And Loss
MCQs Math


Question:     Find the cost price, if a dealer earns a profit of 305% by selling a plot for $24340.50


Correct Answer  6010

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) = $24340.5

And, the profit = 305%

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 + 305 × 24340.5

= 100 × 24340.5/405

= 2434050/405 = 6010

Thus, the Cost Price (CP) = $6010 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 = 305%

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

= 305% of m

= 305% × m

= 305/100 × m

⇒ Profit = 305 m/100

Calculation of Cost Price (CP)

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

⇒ 24340.5 = m + 305 m/100

⇒ 24340.5 = 100 m + 305 m/100

⇒ 24340.5 = 405 m/100

After cross multiplication, we get

24340.5 × 100 = 405 m

⇒ 405 m = 24340.5 × 100

⇒ m = 24340.5 × 100/405

⇒ m = 2434050/405 = 6010

⇒ m = 6010

Thus, the Cost Price (CP) = $6010 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) = $24340.5

And, the profit = 305%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 305% of 100 = 305

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

⇒ Sale Price (SP) = 100 + 305

⇒ Sale Price (SP) = 405

∵ If the Sale Price (SP) is 405, then the Cost Price (CP) = 100

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

= 100/405

∴ If the Sale Price (SP) is 24340.5, then the Cost Price (CP)

= 100/405 × 24340.5

= 100 × 24340.5/405

= 2434050/405 = 6010

Thus, the Cost Price (CP) = $6010 Answer

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

Given, the sale price (SP) = $24340.5

And, the profit = 305%

Then, the Cost Price (CP) = ?

SP = 405% of CP

⇒ SP = 405/100 × CP

⇒ 24340.5 = 405 CP/100

After cross multiplication

⇒ 24340.5 × 100 = 405 CP

⇒ 405 CP = 24340.5 × 100

⇒ CP = 24340.5 × 100/405

⇒ CP = 2434050/405 = 6010

⇒ CP = $6010 Answer


Similar Questions

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

(2) Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

(3) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(4) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

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

(6) 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?

(7) A trader earns a profit of 170% by selling an article for $8937. Find the cost price.

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

(9) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(10) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.


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