Question:
How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?
Correct Answer
2.86%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 36 articles = $1
The Sale Price (SP) for 35 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 36 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/36
∵ The Sale Price (SP) for 35 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/35
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/35 – 1/36
= 36 – 35/1260
⇒ Profit = 1/1260
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/36, the the profit = 1/1260
∴ When the Cost Price (CP) is 1, then the profit
= 1/1260/1/36
= 1/1260 × 36/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/1260 × 36/1 × 100
= 1 × 36 × 100/1260 × 1
= 3600/1260 = 2.86
Thus, Profit = 2.86% 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 36 articles = $1
And, the Sale Price (SP) of 35 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 36 and 35 = 1260
Now, Let total number of articles purchased = 1260
Here, since the Cost Price of 36 articles = $1
∴ the Cost Price of 1 articles = 1/36
Therefore, the Cost Price of 1260 articles
= 1/36 × 1260⇒ The Cost Price (CP) of 1260 articles = $35And, since the Sale Price of 35 articles = $1
∴ The Sale Price (SP) of 1 article = 1/35
Therefore, the Sale Price of 1260 articles
= 1/35 × 1260 = $36
⇒ The Sale Price (SP) of 1260 articles = $36
Now, the Cost Price (CP) of 1260 articles = $35
And, the Sale Price (SP) of 1260 articles = $36
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)
= 36 – 35 = 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 × 100/35
= 100/35 = 2.86
Thus, profit = 2.86% Answer
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