Question:
How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?
Correct Answer
2.78%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 37 articles = $1
The Sale Price (SP) for 36 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 37 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/37
∵ The Sale Price (SP) for 36 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/36
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/36 – 1/37
= 37 – 36/1332
⇒ Profit = 1/1332
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/37, the the profit = 1/1332
∴ When the Cost Price (CP) is 1, then the profit
= 1/1332/1/37
= 1/1332 × 37/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/1332 × 37/1 × 100
= 1 × 37 × 100/1332 × 1
= 3700/1332 = 2.78
Thus, Profit = 2.78% 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 37 articles = $1
And, the Sale Price (SP) of 36 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 37 and 36 = 1332
Now, Let total number of articles purchased = 1332
Here, since the Cost Price of 37 articles = $1
∴ the Cost Price of 1 articles = 1/37
Therefore, the Cost Price of 1332 articles
= 1/37 × 1332⇒ The Cost Price (CP) of 1332 articles = $36And, since the Sale Price of 36 articles = $1
∴ The Sale Price (SP) of 1 article = 1/36
Therefore, the Sale Price of 1332 articles
= 1/36 × 1332 = $37
⇒ The Sale Price (SP) of 1332 articles = $37
Now, the Cost Price (CP) of 1332 articles = $36
And, the Sale Price (SP) of 1332 articles = $37
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)
= 37 – 36 = 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 × 100/36
= 100/36 = 2.78
Thus, profit = 2.78% Answer
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