Profit And Loss
Math MCQs

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

Correct Answer  $10

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) = $9.9

And, the loss = 1%

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 – 1} × 9.9

= ¹⁰⁰/₉₉ × 9.9

= ⁹⁹⁰/₉₉ = 10

Thus, the Cost Price (CP) = $10 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 = 1%

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

= 1% of m

= 1% × m

= ²/₁₀₀ × m

⇒ loss = ^{1 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

⇒ 9.9 = m – ^{1 m}/₁₀₀

⇒ 9.9 = ^{100 m – 1 m}/₁₀₀

⇒ 9.9 = ^{99 m}/₁₀₀

After cross multiplication, we get

9.9 × 100 = 99 m

⇒ 99 m = 9.9 × 100

⇒ m = ^{9.9 × 100}/₉₉

⇒ m = ^{9.9 × 100}/₉₉

⇒ m = ⁹⁹⁰/₉₉ = 10

Thus, the Cost Price (CP) = $10 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) = $9.9

And, the loss = 1%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 1% of 100 = 1

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

⇒ Sale Price (SP) = 100 – 1

⇒ Sale Price (SP) = 99

∵ If the Sale Price (SP) is 99, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₉₉

∴ If the Sale Price (SP) is 9.9, then the Cost Price (CP)

= ¹⁰⁰/₉₉ × 9.9

= ^{100 × 9.9}/₉₉ = 10

Thus, the Cost Price (CP) = $10 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) = $9.9

And, the loss = 1%

Then, the Cost Price (CP) = ?

SP = 99% of CP

⇒ SP = 99% of CP

⇒ 9.9 = ⁹⁹/₁₀₀ × CP

⇒ 9.9 = ^{99 CP}/₁₀₀

After cross multiplication

⇒ 9.9 × 100 = 99 CP

⇒ 99 CP = 9.9 × 100

⇒ CP = ^{9.9 × 100}/₉₉

⇒ CP = ⁹⁹⁰/₉₉ = 10

⇒ CP = $10 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 = 1%

And the Sale Price = $9.9

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

⇒ 100 – 1% of the Cost Price = $9.9

⇒ 99% of the Cost Price = 9.9

Therefore, 1% of the Cost Price = ^9.9/₉₉

Thus, 100% the Cost Price = ^9.9/₉₉ × 100

= ⁹⁹⁰/₉₉ = 10

Thus the Cost Price (CP) = $10 Answer

Similar Questions

(1) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(2) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(3) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(4) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(5) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(6) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

(7) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(8) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(9) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(10) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.