Profit And Loss
MCQs Math


Question:     A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?


Correct Answer  1810

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) = $3529.5

And, the profit = 95%

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 + 95 × 3529.5

= 100 × 3529.5/195

= 352950/195 = 1810

Thus, the Cost Price (CP) = $1810 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 = 95%

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

= 95% of m

= 95% × m

= 95/100 × m

⇒ Profit = 95 m/100

Calculation of Cost Price (CP)

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

⇒ 3529.5 = m + 95 m/100

⇒ 3529.5 = 100 m + 95 m/100

⇒ 3529.5 = 195 m/100

After cross multiplication, we get

3529.5 × 100 = 195 m

⇒ 195 m = 3529.5 × 100

⇒ m = 3529.5 × 100/195

⇒ m = 352950/195 = 1810

⇒ m = 1810

Thus, the Cost Price (CP) = $1810 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) = $3529.5

And, the profit = 95%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 95% of 100 = 95

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

⇒ Sale Price (SP) = 100 + 95

⇒ Sale Price (SP) = 195

∵ If the Sale Price (SP) is 195, then the Cost Price (CP) = 100

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

= 100/195

∴ If the Sale Price (SP) is 3529.5, then the Cost Price (CP)

= 100/195 × 3529.5

= 100 × 3529.5/195

= 352950/195 = 1810

Thus, the Cost Price (CP) = $1810 Answer

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

Given, the sale price (SP) = $3529.5

And, the profit = 95%

Then, the Cost Price (CP) = ?

SP = 195% of CP

⇒ SP = 195/100 × CP

⇒ 3529.5 = 195 CP/100

After cross multiplication

⇒ 3529.5 × 100 = 195 CP

⇒ 195 CP = 3529.5 × 100

⇒ CP = 3529.5 × 100/195

⇒ CP = 352950/195 = 1810

⇒ CP = $1810 Answer


Similar Questions

(1) Find the cost price, if a trader gets a loss of 62% by selling 10 TV sets for $4639.80

(2) 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.

(3) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(4) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(5) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(6) Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

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

(8) What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?

(9) By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

(10) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.


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