Question:
A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?
Correct Answer
3.13%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 33 articles = $1
The Sale Price (SP) for 32 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 33 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/33
∵ The Sale Price (SP) for 32 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/32
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/32 – 1/33
= 33 – 32/1056
⇒ Profit = 1/1056
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/33, the the profit = 1/1056
∴ When the Cost Price (CP) is 1, then the profit
= 1/1056/1/33
= 1/1056 × 33/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/1056 × 33/1 × 100
= 1 × 33 × 100/1056 × 1
= 3300/1056 = 3.13
Thus, Profit = 3.13% 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 33 articles = $1
And, the Sale Price (SP) of 32 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 33 and 32 = 1056
Now, Let total number of articles purchased = 1056
Here, since the Cost Price of 33 articles = $1
∴ the Cost Price of 1 articles = 1/33
Therefore, the Cost Price of 1056 articles
= 1/33 × 1056⇒ The Cost Price (CP) of 1056 articles = $32And, since the Sale Price of 32 articles = $1
∴ The Sale Price (SP) of 1 article = 1/32
Therefore, the Sale Price of 1056 articles
= 1/32 × 1056 = $33
⇒ The Sale Price (SP) of 1056 articles = $33
Now, the Cost Price (CP) of 1056 articles = $32
And, the Sale Price (SP) of 1056 articles = $33
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)
= 33 – 32 = 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 × 100/32
= 100/32 = 3.13
Thus, profit = 3.13% Answer
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