Profit And Loss
MCQs Math


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


Correct Answer  3310

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) = $8937

And, the profit = 170%

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 + 170 × 8937

= 100 × 8937/270

= 893700/270 = 3310

Thus, the Cost Price (CP) = $3310 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 = 170%

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

= 170% of m

= 170% × m

= 170/100 × m

⇒ Profit = 170 m/100

Calculation of Cost Price (CP)

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

⇒ 8937 = m + 170 m/100

⇒ 8937 = 100 m + 170 m/100

⇒ 8937 = 270 m/100

After cross multiplication, we get

8937 × 100 = 270 m

⇒ 270 m = 8937 × 100

⇒ m = 8937 × 100/270

⇒ m = 893700/270 = 3310

⇒ m = 3310

Thus, the Cost Price (CP) = $3310 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) = $8937

And, the profit = 170%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 170% of 100 = 170

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

⇒ Sale Price (SP) = 100 + 170

⇒ Sale Price (SP) = 270

∵ If the Sale Price (SP) is 270, then the Cost Price (CP) = 100

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

= 100/270

∴ If the Sale Price (SP) is 8937, then the Cost Price (CP)

= 100/270 × 8937

= 100 × 8937/270

= 893700/270 = 3310

Thus, the Cost Price (CP) = $3310 Answer

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

Given, the sale price (SP) = $8937

And, the profit = 170%

Then, the Cost Price (CP) = ?

SP = 270% of CP

⇒ SP = 270/100 × CP

⇒ 8937 = 270 CP/100

After cross multiplication

⇒ 8937 × 100 = 270 CP

⇒ 270 CP = 8937 × 100

⇒ CP = 8937 × 100/270

⇒ CP = 893700/270 = 3310

⇒ CP = $3310 Answer


Similar Questions

(1) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

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

(3) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(4) Find the cost price, if a trader gets a loss of 49% by selling 1500 kg rice for $4901.10

(5) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

(6) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.

(7) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(8) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(9) Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

(10) Find the cost price, if a house broker earns a profit of 365% by selling a plot for $33526.5


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