Profit And Loss
MCQs Math


Question:     If a trader gets a loss of 4% by selling an article for $585.60 then, find the cost price.


Correct Answer  $610

Solution And 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) = $585.6

And, the loss = 4%

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 – 4 × 585.6

= 100/96 × 585.6

= 58560/96 = 610

Thus, the Cost Price (CP) = $610 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 = 4%

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

= 4% of m

= 4% × m

= 2/100 × m

⇒ loss = 4 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

⇒ 585.6 = m – 4 m/100

⇒ 585.6 = 100 m – 4 m/100

⇒ 585.6 = 96 m/100

After cross multiplication, we get

585.6 × 100 = 96 m

⇒ 96 m = 585.6 × 100

⇒ m = 585.6 × 100/96

⇒ m = 585.6 × 100/96

⇒ m = 58560/96 = 610

Thus, the Cost Price (CP) = $610 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) = $585.6

And, the loss = 4%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 4% of 100 = 4

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

⇒ Sale Price (SP) = 100 – 4

⇒ Sale Price (SP) = 96

∵ If the Sale Price (SP) is 96, then the Cost Price (CP) = 100

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

= 100/96

∴ If the Sale Price (SP) is 585.6, then the Cost Price (CP)

= 100/96 × 585.6

= 100 × 585.6/96 = 610

Thus, the Cost Price (CP) = $610 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) = $585.6

And, the loss = 4%

Then, the Cost Price (CP) = ?

SP = 96% of CP

⇒ SP = 96% of CP

⇒ 585.6 = 96/100 × CP

⇒ 585.6 = 96 CP/100

After cross multiplication

⇒ 585.6 × 100 = 96 CP

⇒ 96 CP = 585.6 × 100

⇒ CP = 585.6 × 100/96

⇒ CP = 58560/96 = 610

⇒ CP = $610 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 = 4%

And the Sale Price = $585.6

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

⇒ 100 – 4% of the Cost Price = $585.6

⇒ 96% of the Cost Price = 585.6

Therefore, 1% of the Cost Price = 585.6/96

Thus, 100% the Cost Price = 585.6/96 × 100

= 58560/96 = 610

Thus the Cost Price (CP) = $610 Answer


Similar Questions

(1) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

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

(3) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

(4) A shopkeeper loses 40% by selling an article for $1116.00. For how much should he sell it to get a profit of 39%?

(5) Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

(6) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

(7) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

(8) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(9) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(10) A trader gets a loss of 52% by selling 500 bags of rice for $4900.80. Find the cost price of rice.


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