Question:
Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70
Correct Answer
$410
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) = $397.7
And, the loss = 3%
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 – 3 × 397.7
= 100/97 × 397.7
= 39770/97 = 410
Thus, the Cost Price (CP) = $410 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 = 3%
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
= 3% of m
= 3% × m
= 2/100 × m
⇒ loss = 3 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
⇒ 397.7 = m – 3 m/100
⇒ 397.7 = 100 m – 3 m/100
⇒ 397.7 = 97 m/100
After cross multiplication, we get
397.7 × 100 = 97 m
⇒ 97 m = 397.7 × 100
⇒ m = 397.7 × 100/97
⇒ m = 397.7 × 100/97
⇒ m = 39770/97 = 410
Thus, the Cost Price (CP) = $410 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) = $397.7
And, the loss = 3%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus loss = 3% of 100 = 3
Thus, Sale Price (SP) = Cost Price (CP) – loss
⇒ Sale Price (SP) = 100 – 3
⇒ Sale Price (SP) = 97
∵ If the Sale Price (SP) is 97, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/97
∴ If the Sale Price (SP) is 397.7, then the Cost Price (CP)
= 100/97 × 397.7
= 100 × 397.7/97 = 410
Thus, the Cost Price (CP) = $410 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) = $397.7
And, the loss = 3%
Then, the Cost Price (CP) = ?
SP = 97% of CP
⇒ SP = 97% of CP
⇒ 397.7 = 97/100 × CP
⇒ 397.7 = 97 CP/100
After cross multiplication
⇒ 397.7 × 100 = 97 CP
⇒ 97 CP = 397.7 × 100
⇒ CP = 397.7 × 100/97
⇒ CP = 39770/97 = 410
⇒ CP = $410 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 = 3%
And the Sale Price = $397.7
This means 100 – loss% of the Cost Price = Sale Price
⇒ 100 – 3% of the Cost Price = $397.7
⇒ 97% of the Cost Price = 397.7
Therefore, 1% of the Cost Price = 397.7/97
Thus, 100% the Cost Price = 397.7/97 × 100
= 39770/97 = 410
Thus the Cost Price (CP) = $410 Answer
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