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

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

(3) Find the cost price, if a trader earns a profit of 390% by selling an article for $37779

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

(5) Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724

(6) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?

(7) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

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

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

(10) Find the cost price, if a trader gets a loss of 46% by selling 500 kg rice for $4865.40