Question:
What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?
Correct Answer
1.59%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 64 articles = $1
The Sale Price (SP) for 63 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 64 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/64
∵ The Sale Price (SP) for 63 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/63
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/63 – 1/64
= 64 – 63/4032
⇒ Profit = 1/4032
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/64, the the profit = 1/4032
∴ When the Cost Price (CP) is 1, then the profit
= 1/4032/1/64
= 1/4032 × 64/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/4032 × 64/1 × 100
= 1 × 64 × 100/4032 × 1
= 6400/4032 = 1.59
Thus, Profit = 1.59% 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 64 articles = $1
And, the Sale Price (SP) of 63 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 64 and 63 = 4032
Now, Let total number of articles purchased = 4032
Here, since the Cost Price of 64 articles = $1
∴ the Cost Price of 1 articles = 1/64
Therefore, the Cost Price of 4032 articles
= 1/64 × 4032⇒ The Cost Price (CP) of 4032 articles = $63And, since the Sale Price of 63 articles = $1
∴ The Sale Price (SP) of 1 article = 1/63
Therefore, the Sale Price of 4032 articles
= 1/63 × 4032 = $64
⇒ The Sale Price (SP) of 4032 articles = $64
Now, the Cost Price (CP) of 4032 articles = $63
And, the Sale Price (SP) of 4032 articles = $64
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)
= 64 – 63 = 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 × 100/63
= 100/63 = 1.59
Thus, profit = 1.59% Answer
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