Profit And Loss
Math MCQs

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

Correct Answer  $3210

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) = $2664.3

And, the loss = 17%

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 – 17} × 2664.3

= ¹⁰⁰/₈₃ × 2664.3

= ²⁶⁶⁴³⁰/₈₃ = 3210

Thus, the Cost Price (CP) = $3210 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 = 17%

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

= 17% of m

= 17% × m

= ²/₁₀₀ × m

⇒ loss = ^{17 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

⇒ 2664.3 = m – ^{17 m}/₁₀₀

⇒ 2664.3 = ^{100 m – 17 m}/₁₀₀

⇒ 2664.3 = ^{83 m}/₁₀₀

After cross multiplication, we get

2664.3 × 100 = 83 m

⇒ 83 m = 2664.3 × 100

⇒ m = ^{2664.3 × 100}/₈₃

⇒ m = ^{2664.3 × 100}/₈₃

⇒ m = ²⁶⁶⁴³⁰/₈₃ = 3210

Thus, the Cost Price (CP) = $3210 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) = $2664.3

And, the loss = 17%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 17% of 100 = 17

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

⇒ Sale Price (SP) = 100 – 17

⇒ Sale Price (SP) = 83

∵ If the Sale Price (SP) is 83, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₈₃

∴ If the Sale Price (SP) is 2664.3, then the Cost Price (CP)

= ¹⁰⁰/₈₃ × 2664.3

= ^{100 × 2664.3}/₈₃ = 3210

Thus, the Cost Price (CP) = $3210 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) = $2664.3

And, the loss = 17%

Then, the Cost Price (CP) = ?

SP = 83% of CP

⇒ SP = 83% of CP

⇒ 2664.3 = ⁸³/₁₀₀ × CP

⇒ 2664.3 = ^{83 CP}/₁₀₀

After cross multiplication

⇒ 2664.3 × 100 = 83 CP

⇒ 83 CP = 2664.3 × 100

⇒ CP = ^{2664.3 × 100}/₈₃

⇒ CP = ²⁶⁶⁴³⁰/₈₃ = 3210

⇒ CP = $3210 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 = 17%

And the Sale Price = $2664.3

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

⇒ 100 – 17% of the Cost Price = $2664.3

⇒ 83% of the Cost Price = 2664.3

Therefore, 1% of the Cost Price = ^2664.3/₈₃

Thus, 100% the Cost Price = ^2664.3/₈₃ × 100

= ²⁶⁶⁴³⁰/₈₃ = 3210

Thus the Cost Price (CP) = $3210 Answer

Similar Questions

(1) Mr. Donald loses 87% by selling an article for $547.30. For how much should he sell it to get a profit of 86%?

(2) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(3) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(4) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?

(5) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(6) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?

(7) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(8) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

(9) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?

(10) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?