Profit And Loss
Math MCQs

Question :    Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

Correct Answer  $12610

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) = $4539.6

And, the loss = 64%

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 – 64} × 4539.6

= ¹⁰⁰/₃₆ × 4539.6

= ⁴⁵³⁹⁶⁰/₃₆ = 12610

Thus, the Cost Price (CP) = $12610 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 = 64%

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

= 64% of m

= 64% × m

= ⁶⁴/₁₀₀ × m

⇒ loss = ^{64 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

⇒ 4539.6 = m – ^{64 m}/₁₀₀

⇒ 4539.6 = ^{100 m – 64 m}/₁₀₀

⇒ 4539.6 = ^{36 m}/₁₀₀

After cross multiplication, we get

4539.6 × 100 = 36 m

⇒ 36 m = 4539.6 × 100

⇒ m = ^{4539.6 × 100}/₃₆

⇒ m = ^{4539.6 × 100}/₃₆

⇒ m = ⁴⁵³⁹⁶⁰/₃₆ = 12610

Thus, the Cost Price (CP) = $12610 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) = $4539.6

And, the loss = 64%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 64% of 100 = 64

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

⇒ Sale Price (SP) = 100 – 64

⇒ Sale Price (SP) = 36

∵ If the Sale Price (SP) is 36, then the Cost Price (CP) = 100

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

= ¹⁰⁰/₃₆

∴ If the Sale Price (SP) is 4539.6, then the Cost Price (CP)

= ¹⁰⁰/₃₆ × 4539.6

= ^{100 × 4539.6}/₃₆ = 12610

Thus, the Cost Price (CP) = $12610 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) = $4539.6

And, the loss = 64%

Then, the Cost Price (CP) = ?

SP = 36% of CP

⇒ SP = 36% of CP

⇒ 4539.6 = ³⁶/₁₀₀ × CP

⇒ 4539.6 = ^{36 CP}/₁₀₀

After cross multiplication

⇒ 4539.6 × 100 = 36 CP

⇒ 36 CP = 4539.6 × 100

⇒ CP = ^{4539.6 × 100}/₃₆

⇒ CP = ⁴⁵³⁹⁶⁰/₃₆ = 12610

⇒ CP = $12610 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 = 64%

And the Sale Price = $4539.6

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

⇒ 100 – 64% of the Cost Price = $4539.6

⇒ 36% of the Cost Price = 4539.6

Therefore, 1% of the Cost Price = ^4539.6/₃₆

Thus, 100% the Cost Price = ^4539.6/₃₆ × 100

= ⁴⁵³⁹⁶⁰/₃₆ = 12610

Thus the Cost Price (CP) = $12610 Answer

Similar Questions

(1) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(2) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.

(3) If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

(4) If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.

(5) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

(6) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(7) 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.?

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

(9) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

(10) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.