Profit And Loss
MCQs Math


Question:     If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?


Correct Answer  510

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) = $663

And, the profit = 30%

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 + 30 × 663

= 100 × 663/130

= 66300/130 = 510

Thus, the Cost Price (CP) = $510 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 = 30%

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

= 30% of m

= 30% × m

= 30/100 × m

⇒ Profit = 30 m/100

Calculation of Cost Price (CP)

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

⇒ 663 = m + 30 m/100

⇒ 663 = 100 m + 30 m/100

⇒ 663 = 130 m/100

After cross multiplication, we get

663 × 100 = 130 m

⇒ 130 m = 663 × 100

⇒ m = 663 × 100/130

⇒ m = 66300/130 = 510

⇒ m = 510

Thus, the Cost Price (CP) = $510 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) = $663

And, the profit = 30%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 30% of 100 = 30

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

⇒ Sale Price (SP) = 100 + 30

⇒ Sale Price (SP) = 130

∵ If the Sale Price (SP) is 130, then the Cost Price (CP) = 100

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

= 100/130

∴ If the Sale Price (SP) is 663, then the Cost Price (CP)

= 100/130 × 663

= 100 × 663/130

= 66300/130 = 510

Thus, the Cost Price (CP) = $510 Answer

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

Given, the sale price (SP) = $663

And, the profit = 30%

Then, the Cost Price (CP) = ?

SP = 130% of CP

⇒ SP = 130/100 × CP

⇒ 663 = 130 CP/100

After cross multiplication

⇒ 663 × 100 = 130 CP

⇒ 130 CP = 663 × 100

⇒ CP = 663 × 100/130

⇒ CP = 66300/130 = 510

⇒ CP = $510 Answer


Similar Questions

(1) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

(2) A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?

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

(5) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?

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

(7) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

(8) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

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

(10) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706


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