Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 68% by selling five bags of rice for $4291.20

Correct Answer  $13410

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) = $4291.2

And, the loss = 68%

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 – 68} × 4291.2

= ¹⁰⁰/₃₂ × 4291.2

= ⁴²⁹¹²⁰/₃₂ = 13410

Thus, the Cost Price (CP) = $13410 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 = 68%

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

= 68% of m

= 68% × m

= ⁶⁸/₁₀₀ × m

⇒ loss = ^{68 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

⇒ 4291.2 = m – ^{68 m}/₁₀₀

⇒ 4291.2 = ^{100 m – 68 m}/₁₀₀

⇒ 4291.2 = ^{32 m}/₁₀₀

After cross multiplication, we get

4291.2 × 100 = 32 m

⇒ 32 m = 4291.2 × 100

⇒ m = ^{4291.2 × 100}/₃₂

⇒ m = ^{4291.2 × 100}/₃₂

⇒ m = ⁴²⁹¹²⁰/₃₂ = 13410

Thus, the Cost Price (CP) = $13410 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) = $4291.2

And, the loss = 68%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 68% of 100 = 68

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

⇒ Sale Price (SP) = 100 – 68

⇒ Sale Price (SP) = 32

∵ If the Sale Price (SP) is 32, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₂

∴ If the Sale Price (SP) is 4291.2, then the Cost Price (CP)

= ¹⁰⁰/₃₂ × 4291.2

= ^{100 × 4291.2}/₃₂ = 13410

Thus, the Cost Price (CP) = $13410 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) = $4291.2

And, the loss = 68%

Then, the Cost Price (CP) = ?

SP = 32% of CP

⇒ SP = 32% of CP

⇒ 4291.2 = ³²/₁₀₀ × CP

⇒ 4291.2 = ^{32 CP}/₁₀₀

After cross multiplication

⇒ 4291.2 × 100 = 32 CP

⇒ 32 CP = 4291.2 × 100

⇒ CP = ^{4291.2 × 100}/₃₂

⇒ CP = ⁴²⁹¹²⁰/₃₂ = 13410

⇒ CP = $13410 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 = 68%

And the Sale Price = $4291.2

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

⇒ 100 – 68% of the Cost Price = $4291.2

⇒ 32% of the Cost Price = 4291.2

Therefore, 1% of the Cost Price = ^4291.2/₃₂

Thus, 100% the Cost Price = ^4291.2/₃₂ × 100

= ⁴²⁹¹²⁰/₃₂ = 13410

Thus the Cost Price (CP) = $13410 Answer

Similar Questions

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

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(5) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

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(8) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(9) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

(10) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.