Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 41% by selling an article for $4725.90

Correct Answer  $8010

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) = $4725.9

And, the loss = 41%

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 – 41} × 4725.9

= ¹⁰⁰/₅₉ × 4725.9

= ⁴⁷²⁵⁹⁰/₅₉ = 8010

Thus, the Cost Price (CP) = $8010 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 = 41%

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

= 41% of m

= 41% × m

= ⁴¹/₁₀₀ × m

⇒ loss = ^{41 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

⇒ 4725.9 = m – ^{41 m}/₁₀₀

⇒ 4725.9 = ^{100 m – 41 m}/₁₀₀

⇒ 4725.9 = ^{59 m}/₁₀₀

After cross multiplication, we get

4725.9 × 100 = 59 m

⇒ 59 m = 4725.9 × 100

⇒ m = ^{4725.9 × 100}/₅₉

⇒ m = ^{4725.9 × 100}/₅₉

⇒ m = ⁴⁷²⁵⁹⁰/₅₉ = 8010

Thus, the Cost Price (CP) = $8010 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) = $4725.9

And, the loss = 41%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 41% of 100 = 41

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

⇒ Sale Price (SP) = 100 – 41

⇒ Sale Price (SP) = 59

∵ If the Sale Price (SP) is 59, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₅₉

∴ If the Sale Price (SP) is 4725.9, then the Cost Price (CP)

= ¹⁰⁰/₅₉ × 4725.9

= ^{100 × 4725.9}/₅₉ = 8010

Thus, the Cost Price (CP) = $8010 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) = $4725.9

And, the loss = 41%

Then, the Cost Price (CP) = ?

SP = 59% of CP

⇒ SP = 59% of CP

⇒ 4725.9 = ⁵⁹/₁₀₀ × CP

⇒ 4725.9 = ^{59 CP}/₁₀₀

After cross multiplication

⇒ 4725.9 × 100 = 59 CP

⇒ 59 CP = 4725.9 × 100

⇒ CP = ^{4725.9 × 100}/₅₉

⇒ CP = ⁴⁷²⁵⁹⁰/₅₉ = 8010

⇒ CP = $8010 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 = 41%

And the Sale Price = $4725.9

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

⇒ 100 – 41% of the Cost Price = $4725.9

⇒ 59% of the Cost Price = 4725.9

Therefore, 1% of the Cost Price = ^4725.9/₅₉

Thus, 100% the Cost Price = ^4725.9/₅₉ × 100

= ⁴⁷²⁵⁹⁰/₅₉ = 8010

Thus the Cost Price (CP) = $8010 Answer

Similar Questions

(1) Mrs. Rosy loses 25% by selling her stock shares for $832.50. For how much should she sell them to get a profit of 24%?

(2) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.

(3) If a trader gets a loss of 66% by selling ten TV sets for $4423.40 then find the cost price of all those TV sets

(4) Find the cost price, if a broker earns a profit of 370% by selling an old house for $34357

(5) 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?

(6) Find the earnings percentage if a vendor buys 49 articles for $1 and sells 48 articles for $1.

(7) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(8) If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.

(9) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

(10) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.