Question : Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.
Correct Answer 3.33%
Solution & Explanation
Solution
Given,
The Cost Price (CP) for 31 articles = $1
The Sale Price (SP) for 30 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 31 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/31
∵ The Sale Price (SP) for 30 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/30
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/30 – 1/31
= 31 – 30/930
⇒ Profit = 1/930
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/31, the the profit = 1/930
∴ When the Cost Price (CP) is 1, then the profit
= 1/930/1/31
= 1/930 × 31/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/930 × 31/1 × 100
= 1 × 31 × 100/930 × 1
= 3100/930 = 3.33
Thus, Profit = 3.33% 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 31 articles = $1
And, the Sale Price (SP) of 30 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 31 and 30 = 930
Now, Let total number of articles purchased = 930
Here, since the Cost Price of 31 articles = $1
∴ the Cost Price of 1 articles = 1/31
Therefore, the Cost Price of 930 articles
= 1/31 × 930⇒ The Cost Price (CP) of 930 articles = $30And, since the Sale Price of 30 articles = $1
∴ The Sale Price (SP) of 1 article = 1/30
Therefore, the Sale Price of 930 articles
= 1/30 × 930 = $31
⇒ The Sale Price (SP) of 930 articles = $31
Now, the Cost Price (CP) of 930 articles = $30
And, the Sale Price (SP) of 930 articles = $31
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)
= 31 – 30 = 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 × 100/30
= 100/30 = 3.33
Thus, profit = 3.33% Answer
Similar Questions
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(2) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.
(4) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.
(5) Find the cost price, if a trader gets a loss of 45% by selling 800 bags of fruits for $4845.50
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