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) Find the cost price, if a dealer earns a profit of 345% by selling some goods for $30304.5

(2) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718

(3) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(4) What will be profit percent if a peddler buys 12 kiwis for $1 and sells 11 kiwis for $1?

(5) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

(6) If a trader earns a profit of 10% by selling rice for $121 per kg, then find the cost price of the rice

(7) If a broker gets a loss of 22% by selling 100 shares for $3283.80, then find the cost price of those shares.

(8) If a peddler bought 71 paper clips for $1 and sold 70 paper clips for $1 then, find the profit in percent.

(9) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

(10) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.


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