Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 36% by selling 500 packets of fruits for $4486.40

Correct Answer  $7010

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) = $4486.4

And, the loss = 36%

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 – 36} × 4486.4

= ¹⁰⁰/₆₄ × 4486.4

= ⁴⁴⁸⁶⁴⁰/₆₄ = 7010

Thus, the Cost Price (CP) = $7010 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 = 36%

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

= 36% of m

= 36% × m

= ²/₁₀₀ × m

⇒ loss = ^{36 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

⇒ 4486.4 = m – ^{36 m}/₁₀₀

⇒ 4486.4 = ^{100 m – 36 m}/₁₀₀

⇒ 4486.4 = ^{64 m}/₁₀₀

After cross multiplication, we get

4486.4 × 100 = 64 m

⇒ 64 m = 4486.4 × 100

⇒ m = ^{4486.4 × 100}/₆₄

⇒ m = ^{4486.4 × 100}/₆₄

⇒ m = ⁴⁴⁸⁶⁴⁰/₆₄ = 7010

Thus, the Cost Price (CP) = $7010 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) = $4486.4

And, the loss = 36%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 36% of 100 = 36

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

⇒ Sale Price (SP) = 100 – 36

⇒ Sale Price (SP) = 64

∵ If the Sale Price (SP) is 64, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₆₄

∴ If the Sale Price (SP) is 4486.4, then the Cost Price (CP)

= ¹⁰⁰/₆₄ × 4486.4

= ^{100 × 4486.4}/₆₄ = 7010

Thus, the Cost Price (CP) = $7010 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) = $4486.4

And, the loss = 36%

Then, the Cost Price (CP) = ?

SP = 64% of CP

⇒ SP = 64% of CP

⇒ 4486.4 = ⁶⁴/₁₀₀ × CP

⇒ 4486.4 = ^{64 CP}/₁₀₀

After cross multiplication

⇒ 4486.4 × 100 = 64 CP

⇒ 64 CP = 4486.4 × 100

⇒ CP = ^{4486.4 × 100}/₆₄

⇒ CP = ⁴⁴⁸⁶⁴⁰/₆₄ = 7010

⇒ CP = $7010 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 = 36%

And the Sale Price = $4486.4

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

⇒ 100 – 36% of the Cost Price = $4486.4

⇒ 64% of the Cost Price = 4486.4

Therefore, 1% of the Cost Price = ^4486.4/₆₄

Thus, 100% the Cost Price = ^4486.4/₆₄ × 100

= ⁴⁴⁸⁶⁴⁰/₆₄ = 7010

Thus the Cost Price (CP) = $7010 Answer

Similar Questions

(1) Mr. Jojo buys 30 articles for $1 and sells 29 articles for $1. Find the profit in percent.

(2) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

(3) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?

(4) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?

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

(6) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

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

(8) A dealer loses 57% by selling an article for $1165.30. For how much should he sell it to get a profit of 56%?

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

(10) To get a profit of 15% Mr. John should sell his old bicycle for how much, if he loses 16% by selling it for $554.40?