Question:
If a trader earns a profit of 45% by selling an article for $1174.5, then find the cost price.
Correct Answer
810
Solution And Explanation
Solution
Finding the cost price if the sale price and profit percent are known
The cost price (CP) can be found using the formula, algebraic method, using shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want.
Finding the cost price using the formula when the sale price and profit percent are known
Given, the sale price (SP) = $1174.5
And, the profit = 45%
Then, the Cost Price (CP) = ?
Formula to find the cost price when the sale price and profit percent are known
Cost Price (CP) = 100/100 + gain% × SP
Thus, the Cost Price (CP)
= 100/100 + 45 × 1174.5
= 100 × 1174.5/145
= 117450/145 = 810
Thus, the Cost Price (CP) = $810 Answer
Finding the cost price (CP) using the Algebraic Method when the Sale Pric (SP) and the profit percent are given
Let the Cost Price (CP) = m
Here given profit = 45%
Calculation of Profit
Profit is calculated on cost price (CP)
Formula to find the Profit = Profit% of CP
Thus, profit on the cost price of m
= 45% of m
= 45% × m
= 45/100 × m
⇒ Profit = 45 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 1174.5 = m + 45 m/100
⇒ 1174.5 = 100 m + 45 m/100
⇒ 1174.5 = 145 m/100
After cross multiplication, we get
1174.5 × 100 = 145 m
⇒ 145 m = 1174.5 × 100
⇒ m = 1174.5 × 100/145
⇒ m = 117450/145 = 810
⇒ m = 810
Thus, the Cost Price (CP) = $810 Answer
Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the profit percent are given
Given, the sale price (SP) = $1174.5
And, the profit = 45%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 45% of 100 = 45
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 45
⇒ Sale Price (SP) = 145
∵ If the Sale Price (SP) is 145, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/145
∴ If the Sale Price (SP) is 1174.5, then the Cost Price (CP)
= 100/145 × 1174.5
= 100 × 1174.5/145
= 117450/145 = 810
Thus, the Cost Price (CP) = $810 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $1174.5
And, the profit = 45%
Then, the Cost Price (CP) = ?
SP = 145% of CP
⇒ SP = 145/100 × CP
⇒ 1174.5 = 145 CP/100
After cross multiplication
⇒ 1174.5 × 100 = 145 CP
⇒ 145 CP = 1174.5 × 100
⇒ CP = 1174.5 × 100/145
⇒ CP = 117450/145 = 810
⇒ CP = $810 Answer
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