Profit And Loss
Math MCQs

Question :    Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?

Correct Answer  $1810

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) = $1629

And, the loss = 10%

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 – 10} × 1629

= ¹⁰⁰/₉₀ × 1629

= ¹⁶²⁹⁰⁰/₉₀ = 1810

Thus, the Cost Price (CP) = $1810 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 = 10%

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

= 10% of m

= 10% × m

= ²/₁₀₀ × m

⇒ loss = ^{10 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

⇒ 1629 = m – ^{10 m}/₁₀₀

⇒ 1629 = ^{100 m – 10 m}/₁₀₀

⇒ 1629 = ^{90 m}/₁₀₀

After cross multiplication, we get

1629 × 100 = 90 m

⇒ 90 m = 1629 × 100

⇒ m = ^{1629 × 100}/₉₀

⇒ m = ^{1629 × 100}/₉₀

⇒ m = ¹⁶²⁹⁰⁰/₉₀ = 1810

Thus, the Cost Price (CP) = $1810 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) = $1629

And, the loss = 10%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 10% of 100 = 10

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

⇒ Sale Price (SP) = 100 – 10

⇒ Sale Price (SP) = 90

∵ If the Sale Price (SP) is 90, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₉₀

∴ If the Sale Price (SP) is 1629, then the Cost Price (CP)

= ¹⁰⁰/₉₀ × 1629

= ^{100 × 1629}/₉₀ = 1810

Thus, the Cost Price (CP) = $1810 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) = $1629

And, the loss = 10%

Then, the Cost Price (CP) = ?

SP = 90% of CP

⇒ SP = 90% of CP

⇒ 1629 = ⁹⁰/₁₀₀ × CP

⇒ 1629 = ^{90 CP}/₁₀₀

After cross multiplication

⇒ 1629 × 100 = 90 CP

⇒ 90 CP = 1629 × 100

⇒ CP = ^{1629 × 100}/₉₀

⇒ CP = ¹⁶²⁹⁰⁰/₉₀ = 1810

⇒ CP = $1810 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 = 10%

And the Sale Price = $1629

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

⇒ 100 – 10% of the Cost Price = $1629

⇒ 90% of the Cost Price = 1629

Therefore, 1% of the Cost Price = ¹⁶²⁹/₉₀

Thus, 100% the Cost Price = ¹⁶²⁹/₉₀ × 100

= ¹⁶²⁹⁰⁰/₉₀ = 1810

Thus the Cost Price (CP) = $1810 Answer

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