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) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(2) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(3) A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?

(4) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.

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

(6) If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

(7) 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?

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

(9) Peter loses 32% by selling an article for $992.80. For how much should he sell it to get a profit of 31%?

(10) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.