Profit And Loss
Math MCQs

Question :    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

Correct Answer  $13010

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) = $4423.4

And, the loss = 66%

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 – 66} × 4423.4

= ¹⁰⁰/₃₄ × 4423.4

= ⁴⁴²³⁴⁰/₃₄ = 13010

Thus, the Cost Price (CP) = $13010 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 = 66%

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

= 66% of m

= 66% × m

= ⁶⁶/₁₀₀ × m

⇒ loss = ^{66 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

⇒ 4423.4 = m – ^{66 m}/₁₀₀

⇒ 4423.4 = ^{100 m – 66 m}/₁₀₀

⇒ 4423.4 = ^{34 m}/₁₀₀

After cross multiplication, we get

4423.4 × 100 = 34 m

⇒ 34 m = 4423.4 × 100

⇒ m = ^{4423.4 × 100}/₃₄

⇒ m = ^{4423.4 × 100}/₃₄

⇒ m = ⁴⁴²³⁴⁰/₃₄ = 13010

Thus, the Cost Price (CP) = $13010 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) = $4423.4

And, the loss = 66%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 66% of 100 = 66

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

⇒ Sale Price (SP) = 100 – 66

⇒ Sale Price (SP) = 34

∵ If the Sale Price (SP) is 34, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₄

∴ If the Sale Price (SP) is 4423.4, then the Cost Price (CP)

= ¹⁰⁰/₃₄ × 4423.4

= ^{100 × 4423.4}/₃₄ = 13010

Thus, the Cost Price (CP) = $13010 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) = $4423.4

And, the loss = 66%

Then, the Cost Price (CP) = ?

SP = 34% of CP

⇒ SP = 34% of CP

⇒ 4423.4 = ³⁴/₁₀₀ × CP

⇒ 4423.4 = ^{34 CP}/₁₀₀

After cross multiplication

⇒ 4423.4 × 100 = 34 CP

⇒ 34 CP = 4423.4 × 100

⇒ CP = ^{4423.4 × 100}/₃₄

⇒ CP = ⁴⁴²³⁴⁰/₃₄ = 13010

⇒ CP = $13010 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 = 66%

And the Sale Price = $4423.4

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

⇒ 100 – 66% of the Cost Price = $4423.4

⇒ 34% of the Cost Price = 4423.4

Therefore, 1% of the Cost Price = ^4423.4/₃₄

Thus, 100% the Cost Price = ^4423.4/₃₄ × 100

= ⁴⁴²³⁴⁰/₃₄ = 13010

Thus the Cost Price (CP) = $13010 Answer

Similar Questions

(1) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?

(2) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(3) By selling an article for $15443.50, Mrs. Linda earns a profit of 235%. What was the cost price?

(4) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(5) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(6) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

(7) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

(8) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.

(9) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(10) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?