Profit And Loss
Math MCQs

Question :    By selling some items for $1788.90 a vendor gets a loss of 11%. Find the cost price of those items.

Correct Answer  $2010

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) = $1788.9

And, the loss = 11%

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 – 11} × 1788.9

= ¹⁰⁰/₈₉ × 1788.9

= ¹⁷⁸⁸⁹⁰/₈₉ = 2010

Thus, the Cost Price (CP) = $2010 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 = 11%

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

= 11% of m

= 11% × m

= ²/₁₀₀ × m

⇒ loss = ^{11 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

⇒ 1788.9 = m – ^{11 m}/₁₀₀

⇒ 1788.9 = ^{100 m – 11 m}/₁₀₀

⇒ 1788.9 = ^{89 m}/₁₀₀

After cross multiplication, we get

1788.9 × 100 = 89 m

⇒ 89 m = 1788.9 × 100

⇒ m = ^{1788.9 × 100}/₈₉

⇒ m = ^{1788.9 × 100}/₈₉

⇒ m = ¹⁷⁸⁸⁹⁰/₈₉ = 2010

Thus, the Cost Price (CP) = $2010 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) = $1788.9

And, the loss = 11%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 11% of 100 = 11

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

⇒ Sale Price (SP) = 100 – 11

⇒ Sale Price (SP) = 89

∵ If the Sale Price (SP) is 89, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₈₉

∴ If the Sale Price (SP) is 1788.9, then the Cost Price (CP)

= ¹⁰⁰/₈₉ × 1788.9

= ^{100 × 1788.9}/₈₉ = 2010

Thus, the Cost Price (CP) = $2010 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) = $1788.9

And, the loss = 11%

Then, the Cost Price (CP) = ?

SP = 89% of CP

⇒ SP = 89% of CP

⇒ 1788.9 = ⁸⁹/₁₀₀ × CP

⇒ 1788.9 = ^{89 CP}/₁₀₀

After cross multiplication

⇒ 1788.9 × 100 = 89 CP

⇒ 89 CP = 1788.9 × 100

⇒ CP = ^{1788.9 × 100}/₈₉

⇒ CP = ¹⁷⁸⁸⁹⁰/₈₉ = 2010

⇒ CP = $2010 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 = 11%

And the Sale Price = $1788.9

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

⇒ 100 – 11% of the Cost Price = $1788.9

⇒ 89% of the Cost Price = 1788.9

Therefore, 1% of the Cost Price = ^1788.9/₈₉

Thus, 100% the Cost Price = ^1788.9/₈₉ × 100

= ¹⁷⁸⁸⁹⁰/₈₉ = 2010

Thus the Cost Price (CP) = $2010 Answer

Similar Questions

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(7) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(8) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

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

(10) Find the cost price, if a trader gets a loss of 49% by selling 1500 kg rice for $4901.10