Question:
Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?
Correct Answer
410
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) = $512.5
And, the profit = 25%
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 + 25 × 512.5
= 100 × 512.5/125
= 51250/125 = 410
Thus, the Cost Price (CP) = $410 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 = 25%
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
= 25% of m
= 25% × m
= 25/100 × m
⇒ Profit = 25 m/100
Calculation of Cost Price (CP)
The Sale Price (SP) = Cost Price (CP) + Profit
⇒ 512.5 = m + 25 m/100
⇒ 512.5 = 100 m + 25 m/100
⇒ 512.5 = 125 m/100
After cross multiplication, we get
512.5 × 100 = 125 m
⇒ 125 m = 512.5 × 100
⇒ m = 512.5 × 100/125
⇒ m = 51250/125 = 410
⇒ m = 410
Thus, the Cost Price (CP) = $410 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) = $512.5
And, the profit = 25%
Then, the Cost Price (CP) = ?
Let Cost Price (CP) = 100
Thus profit = 25% of 100 = 25
Thus, Sale Price (SP) = Cost Price (CP) + Profit
⇒ Sale Price (SP) = 100 + 25
⇒ Sale Price (SP) = 125
∵ If the Sale Price (SP) is 125, then the Cost Price (CP) = 100
∴ If the Sale Price (SP) is 1, then the Cost Price (CP)
= 100/125
∴ If the Sale Price (SP) is 512.5, then the Cost Price (CP)
= 100/125 × 512.5
= 100 × 512.5/125
= 51250/125 = 410
Thus, the Cost Price (CP) = $410 Answer
Shortcut Method to find Cost Price (CP) when SP and profit percent are known
Given, the sale price (SP) = $512.5
And, the profit = 25%
Then, the Cost Price (CP) = ?
SP = 125% of CP
⇒ SP = 125/100 × CP
⇒ 512.5 = 125 CP/100
After cross multiplication
⇒ 512.5 × 100 = 125 CP
⇒ 125 CP = 512.5 × 100
⇒ CP = 512.5 × 100/125
⇒ CP = 51250/125 = 410
⇒ CP = $410 Answer
Similar Questions
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(2) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.
(3) 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.
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(5) Find the cost price, if a trader gets a loss of 67% by selling ten bags of apple for $4359.30
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(7) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.
(8) 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.?
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