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

(1) Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

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

(3) Bill sold a bicycle for $640. If he purchased it at $800, then calculate his loss and loss percent in this sale.

(4) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?

(5) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

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

(7) Mr. Donald loses 88% by selling an article for $511.20. For how much should he sell it to get a profit of 87%?

(8) How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?

(9) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(10) After selling a furniture for $481.60 a shopkeeper gets a loss of 14%. In order to get a profit of 13% he should sell in for how much?