Profit And Loss
Math MCQs

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

Correct Answer  1210

Solution & 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) = $1996.5

And, the profit = 65%

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 + 65} × 1996.5

= ^{100 × 1996.5}/₁₆₅

= ¹⁹⁹⁶⁵⁰/₁₆₅ = 1210

Thus, the Cost Price (CP) = $1210 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 = 65%

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

= 65% of m

= 65% × m

= ⁶⁵/₁₀₀ × m

⇒ Profit = ^{65 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 1996.5 = m + ^{65 m}/₁₀₀

⇒ 1996.5 = ^{100 m + 65 m}/₁₀₀

⇒ 1996.5 = ^{165 m}/₁₀₀

After cross multiplication, we get

1996.5 × 100 = 165 m

⇒ 165 m = 1996.5 × 100

⇒ m = ^{1996.5 × 100}/₁₆₅

⇒ m = ¹⁹⁹⁶⁵⁰/₁₆₅ = 1210

⇒ m = 1210

Thus, the Cost Price (CP) = $1210 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) = $1996.5

And, the profit = 65%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 65% of 100 = 65

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

⇒ Sale Price (SP) = 100 + 65

⇒ Sale Price (SP) = 165

∵ If the Sale Price (SP) is 165, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₁₆₅

∴ If the Sale Price (SP) is 1996.5, then the Cost Price (CP)

= ¹⁰⁰/₁₆₅ × 1996.5

= ^{100 × 1996.5}/₁₆₅

= ¹⁹⁹⁶⁵⁰/₁₆₅ = 1210

Thus, the Cost Price (CP) = $1210 Answer

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

Given, the sale price (SP) = $1996.5

And, the profit = 65%

Then, the Cost Price (CP) = ?

SP = 165% of CP

⇒ SP = ¹⁶⁵/₁₀₀ × CP

⇒ 1996.5 = ^{165 CP}/₁₀₀

After cross multiplication

⇒ 1996.5 × 100 = 165 CP

⇒ 165 CP = 1996.5 × 100

⇒ CP = ^{1996.5 × 100}/₁₆₅

⇒ CP = ¹⁹⁹⁶⁵⁰/₁₆₅ = 1210

⇒ CP = $1210 Answer

Similar Questions

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

(3) Mr. James gets a profit of 180% by selling a plot for $9828. Find the cost price of that plot.

(4) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(5) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

(6) Mr. Joseph loses 5% by selling an article for $104.50. For how much should he sell it to get a profit of 4%?

(7) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

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

(9) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

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