Question:
A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.
Correct Answer
14.29%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 8 articles = $1
The Sale Price (SP) for 7 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 8 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/8
∵ The Sale Price (SP) for 7 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/7
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/7 – 1/8
= 8 – 7/56
⇒ Profit = 1/56
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/8, the the profit = 1/56
∴ When the Cost Price (CP) is 1, then the profit
= 1/56/1/8
= 1/56 × 8/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/56 × 8/1 × 100
= 1 × 8 × 100/56 × 1
= 800/56 = 14.29
Thus, Profit = 14.29% 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 8 articles = $1
And, the Sale Price (SP) of 7 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 8 and 7 = 56
Now, Let total number of articles purchased = 56
Here, since the Cost Price of 8 articles = $1
∴ the Cost Price of 1 articles = 1/8
Therefore, the Cost Price of 56 articles
= 1/8 × 56⇒ The Cost Price (CP) of 56 articles = $7And, since the Sale Price of 7 articles = $1
∴ The Sale Price (SP) of 1 article = 1/7
Therefore, the Sale Price of 56 articles
= 1/7 × 56 = $8
⇒ The Sale Price (SP) of 56 articles = $8
Now, the Cost Price (CP) of 56 articles = $7
And, the Sale Price (SP) of 56 articles = $8
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)
= 8 – 7 = 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 × 100/7
= 100/7 = 14.29
Thus, profit = 14.29% Answer
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