Question:
If a shopkeeper earns a profit of 5% by selling an article at $210, then find the cost price of that article.
Correct Answer
200
Solution And Explanation
Solution
Given, the sale price (SP) = $210
And, the profit = 5%
Then, the Cost Price (CP) = ?
Finding the cost price (CP) using formula when the SP and the profit are given
The formula to find the Cost Price, when the Sale Price (SP) and the Profit are known
Cost Price (CP) = 100/100 + gain% × SP
Thus, the Cost Price (CP)
= 100/100 + 5 × 210
= 100/105 × 210 2
= 100 × 2 = 200
Thus, the Cost Price (CP) = $200 Answer
Finding the cost price (CP) using Algebraic Method when the Sale Pric (SP) and the profit are given
Given, the sale price (SP) = $210
And, the profit = 5%
Then, the Cost Price (CP) = ?
Calculation of Profit
Let the Cost Price (CP) = m
Threfore, profit = Profit% of CP
= 5% of m
= 5% × m
= 5/100 20 × m
= 1/20 × m
⇒ Profit = m/20
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 210 = m + m/20
⇒ 210 = 20 m + m/20
⇒ 210 = 21 m/20
After cross multiplication, we get
21 m = 210 × 20
⇒ m = 210 × 20/21
⇒ m = 210 10 × 20/21
⇒ m = 10 × 20 = 200
Thus, the Cost Price (CP) = $200 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 are given
Given, the sale price (SP) = $210
And, the profit = 5%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 5% of 100 = 5
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 5
⇒ Sale Price (SP) = 105
∵ If the Sale Price (SP) is 105, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/105
∴ If the Sale Price (SP) is 210, then the Cost Price (CP)
= 100/105 × 210
= 100/105 × 210 2
= 100 × 2 = 200
Thus, the Cost Price (CP) = $200 Answer
Shortcut Method to find Cost Price (CP) when SP and profit are known
Given, the sale price (SP) = $210
And, the profit = 5%
Then, the Cost Price (CP) = ?
SP = CP + 5% of CP
⇒ 210 = CP + 5/100 × CP
⇒ 210 = 100 CP + 5 CP/100
⇒ 210 = 105 CP/100
After cross multiplication
⇒ 210 × 100 = 105 CP
⇒ CP = 210 2 × 100/105
⇒ CP = = 2 × 100 = 200
⇒ CP = $200 Answer
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