Profit And Loss
Math MCQs

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

Correct Answer  $7210

Solution & Explanation

Solution

Finding the cost price if the sale price and loss percent are known

The cost price (CP) can be found using the formula, algebraic method, shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want. Here the five methods to solve this problem have been given.

Method (1) Using Formula

Finding the cost price using the formula when the sale price and loss percent are known

Given, the sale price (SP) = $4542.3

And, the loss = 37%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and loss percent are known

Cost Price (CP) = ¹⁰⁰/_{100 – gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 – 37} × 4542.3

= ¹⁰⁰/₆₃ × 4542.3

= ⁴⁵⁴²³⁰/₆₃ = 7210

Thus, the Cost Price (CP) = $7210 Answer

Method (2) Algebraic Method

Finding the cost price (CP) using the Algebraic Method when the Sale Price (SP) and the loss percent are given

Let the Cost Price (CP) = m

Here given loss = 37%

Calculation of loss

The loss and/or profit is calculated on the cost price (CP)

Formula to find the loss when the Cost Price and the Loss% are given

Loss = loss% of CP

Thus, loss on the cost price of m

= Loss% of m

= 37% of m

= 37% × m

= ²/₁₀₀ × m

⇒ loss = ^{37 m}/₁₀₀

Calculation of Cost Price (CP)

Formula to find the Sale Price (SP) when the Cost Price (CP) and the Loss are given

Sale Price (SP) = Cost Price (CP) – Loss

⇒ 4542.3 = m – ^{37 m}/₁₀₀

⇒ 4542.3 = ^{100 m – 37 m}/₁₀₀

⇒ 4542.3 = ^{63 m}/₁₀₀

After cross multiplication, we get

4542.3 × 100 = 63 m

⇒ 63 m = 4542.3 × 100

⇒ m = ^{4542.3 × 100}/₆₃

⇒ m = ^{4542.3 × 100}/₆₃

⇒ m = ⁴⁵⁴²³⁰/₆₃ = 7210

Thus, the Cost Price (CP) = $7210 Answer

Method (3) Unitary Method

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the loss percent are given

Given, the sale price (SP) = $4542.3

And, the loss = 37%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 37% of 100 = 37

Thus, Sale Price (SP) = Cost Price (CP) – loss

⇒ Sale Price (SP) = 100 – 37

⇒ Sale Price (SP) = 63

∵ If the Sale Price (SP) is 63, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₆₃

∴ If the Sale Price (SP) is 4542.3, then the Cost Price (CP)

= ¹⁰⁰/₆₃ × 4542.3

= ^{100 × 4542.3}/₆₃ = 7210

Thus, the Cost Price (CP) = $7210 Answer

Method (4) Shortcut Method (1)

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

Given, the sale price (SP) = $4542.3

And, the loss = 37%

Then, the Cost Price (CP) = ?

SP = 63% of CP

⇒ SP = 63% of CP

⇒ 4542.3 = ⁶³/₁₀₀ × CP

⇒ 4542.3 = ^{63 CP}/₁₀₀

After cross multiplication

⇒ 4542.3 × 100 = 63 CP

⇒ 63 CP = 4542.3 × 100

⇒ CP = ^{4542.3 × 100}/₆₃

⇒ CP = ⁴⁵⁴²³⁰/₆₃ = 7210

⇒ CP = $7210 Answer

Method (5) Shortcut Method (2)

Shortcut Method (2) to find Cost Price (CP) when SP and loss percent are known

Here loss and the Sale Price are given and the Cost Price is to find

Here as given, the loss = 37%

And the Sale Price = $4542.3

This means 100 – loss% of the Cost Price = Sale Price

⇒ 100 – 37% of the Cost Price = $4542.3

⇒ 63% of the Cost Price = 4542.3

Therefore, 1% of the Cost Price = ^4542.3/₆₃

Thus, 100% the Cost Price = ^4542.3/₆₃ × 100

= ⁴⁵⁴²³⁰/₆₃ = 7210

Thus the Cost Price (CP) = $7210 Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

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

(3) If a trader gets a loss of 4% by selling an article for $585.60 then, find the cost price.

(4) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(5) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(6) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?

(7) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70

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

(9) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(10) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00