Question:
Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.
Correct Answer
1.56%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 65 articles = $1
The Sale Price (SP) for 64 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 65 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/65
∵ The Sale Price (SP) for 64 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/64
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/64 – 1/65
= 65 – 64/4160
⇒ Profit = 1/4160
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/65, the the profit = 1/4160
∴ When the Cost Price (CP) is 1, then the profit
= 1/4160/1/65
= 1/4160 × 65/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/4160 × 65/1 × 100
= 1 × 65 × 100/4160 × 1
= 6500/4160 = 1.56
Thus, Profit = 1.56% Answer
Method (2) to find the profit%
Finding the profit percent by taking LCM of the number of articles purchased and sold for the same price
Given, the Cost Price (CP) of 65 articles = $1
And, the Sale Price (SP) of 64 articles = $1
Here, we need to take the LCM of number of articles purchased and sold to make them uniform.
Calculation of the Cost Price (CP) and the Sale Price
The LCM of 65 and 64 = 4160
Now, Let total number of articles purchased = 4160
Here, since the Cost Price of 65 articles = $1
∴ the Cost Price of 1 articles = 1/65
Therefore, the Cost Price of 4160 articles
= 1/65 × 4160⇒ The Cost Price (CP) of 4160 articles = $64And, since the Sale Price of 64 articles = $1
∴ The Sale Price (SP) of 1 article = 1/64
Therefore, the Sale Price of 4160 articles
= 1/64 × 4160 = $65
⇒ The Sale Price (SP) of 4160 articles = $65
Now, the Cost Price (CP) of 4160 articles = $64
And, the Sale Price (SP) of 4160 articles = $65
Calculation of the Profit, when the Cost Price (CP) and the Sale Price (SP) are given
Formula to find the profit when the Cost Price (CP) and the Sale Price (SP) are given
Profit = Sale Price (SP) – Cost Price (CP)
= 65 – 64 = 1
⇒ Profit = $1
Calculation of Profit percent using the formula
Formula to calculate the profit percent
Profit percent = Profit × 100/Cost Price
Thus, profit % = 1 × 100/64
= 100/64 = 1.56
Thus, profit = 1.56% Answer
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