Profit And Loss
Math MCQs

Question :    What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5

Correct Answer  3210

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) = $8506.5

And, the profit = 165%

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 + 165} × 8506.5

= ^{100 × 8506.5}/₂₆₅

= ⁸⁵⁰⁶⁵⁰/₂₆₅ = 3210

Thus, the Cost Price (CP) = $3210 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 = 165%

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

= 165% of m

= 165% × m

= ¹⁶⁵/₁₀₀ × m

⇒ Profit = ^{165 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 8506.5 = m + ^{165 m}/₁₀₀

⇒ 8506.5 = ^{100 m + 165 m}/₁₀₀

⇒ 8506.5 = ^{265 m}/₁₀₀

After cross multiplication, we get

8506.5 × 100 = 265 m

⇒ 265 m = 8506.5 × 100

⇒ m = ^{8506.5 × 100}/₂₆₅

⇒ m = ⁸⁵⁰⁶⁵⁰/₂₆₅ = 3210

⇒ m = 3210

Thus, the Cost Price (CP) = $3210 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) = $8506.5

And, the profit = 165%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 165% of 100 = 165

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

⇒ Sale Price (SP) = 100 + 165

⇒ Sale Price (SP) = 265

∵ If the Sale Price (SP) is 265, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₆₅

∴ If the Sale Price (SP) is 8506.5, then the Cost Price (CP)

= ¹⁰⁰/₂₆₅ × 8506.5

= ^{100 × 8506.5}/₂₆₅

= ⁸⁵⁰⁶⁵⁰/₂₆₅ = 3210

Thus, the Cost Price (CP) = $3210 Answer

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

Given, the sale price (SP) = $8506.5

And, the profit = 165%

Then, the Cost Price (CP) = ?

SP = 265% of CP

⇒ SP = ²⁶⁵/₁₀₀ × CP

⇒ 8506.5 = ^{265 CP}/₁₀₀

After cross multiplication

⇒ 8506.5 × 100 = 265 CP

⇒ 265 CP = 8506.5 × 100

⇒ CP = ^{8506.5 × 100}/₂₆₅

⇒ CP = ⁸⁵⁰⁶⁵⁰/₂₆₅ = 3210

⇒ CP = $3210 Answer

Similar Questions

(1) To earn a profit of 7% Mr. Robert should sell his article for how much if he gets a loss of 8% by selling it for $239.20?

(2) Find the cost price, if a trader gets a loss of 37% by selling 500 packets of fruits for $4542.30

(3) Find the cost price, if a shopkeeper earns a profit of 240% by selling an article for $16014

(4) Find the cost price if a broker earned 375% while dealing a house for $35197.50

(5) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(6) If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

(7) If a shopkeeper gets a loss of 65% by selling five TV sets for $4483.50 then find the cost price of all those TV sets.

(8) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(9) Find the cost price, if a trader gets a loss of 1% by selling an article for $9.9

(10) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90