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
(1) By selling some items for $12741.00 a trader earns a profit of 210%. Find the cost price.
(2) A trader loses 42% by selling an article for $1136.80. For how much should he sell it to get a profit of 41%?
(3) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?
(4) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.
(5) Mr. Jack gets a profit of 195% by selling some articles for $11239.50. What was his cost price?
(6) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.
(7) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5
(8) Bill sold his bicycle at a profit of 15%. If he purchased that bicycle at $200 then find the sale price of the cycle.
(9) Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.
(10) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?