Profit And Loss
Math MCQs

Question :    A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

Correct Answer  3410

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) = $9377.5

And, the profit = 175%

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 + 175} × 9377.5

= ^{100 × 9377.5}/₂₇₅

= ⁹³⁷⁷⁵⁰/₂₇₅ = 3410

Thus, the Cost Price (CP) = $3410 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 = 175%

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

= 175% of m

= 175% × m

= ¹⁷⁵/₁₀₀ × m

⇒ Profit = ^{175 m}/₁₀₀

Calculation of Cost Price (CP)

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

⇒ 9377.5 = m + ^{175 m}/₁₀₀

⇒ 9377.5 = ^{100 m + 175 m}/₁₀₀

⇒ 9377.5 = ^{275 m}/₁₀₀

After cross multiplication, we get

9377.5 × 100 = 275 m

⇒ 275 m = 9377.5 × 100

⇒ m = ^{9377.5 × 100}/₂₇₅

⇒ m = ⁹³⁷⁷⁵⁰/₂₇₅ = 3410

⇒ m = 3410

Thus, the Cost Price (CP) = $3410 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) = $9377.5

And, the profit = 175%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus profit = 175% of 100 = 175

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

⇒ Sale Price (SP) = 100 + 175

⇒ Sale Price (SP) = 275

∵ If the Sale Price (SP) is 275, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₂₇₅

∴ If the Sale Price (SP) is 9377.5, then the Cost Price (CP)

= ¹⁰⁰/₂₇₅ × 9377.5

= ^{100 × 9377.5}/₂₇₅

= ⁹³⁷⁷⁵⁰/₂₇₅ = 3410

Thus, the Cost Price (CP) = $3410 Answer

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

Given, the sale price (SP) = $9377.5

And, the profit = 175%

Then, the Cost Price (CP) = ?

SP = 275% of CP

⇒ SP = ²⁷⁵/₁₀₀ × CP

⇒ 9377.5 = ^{275 CP}/₁₀₀

After cross multiplication

⇒ 9377.5 × 100 = 275 CP

⇒ 275 CP = 9377.5 × 100

⇒ CP = ^{9377.5 × 100}/₂₇₅

⇒ CP = ⁹³⁷⁷⁵⁰/₂₇₅ = 3410

⇒ CP = $3410 Answer

Similar Questions

(1) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.

(2) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(3) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

(4) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?

(5) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(6) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

(7) What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?

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

(9) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

(10) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.