Question:
What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?
Correct Answer
1.72%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 59 articles = $1
The Sale Price (SP) for 58 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 59 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/59
∵ The Sale Price (SP) for 58 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/58
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/58 – 1/59
= 59 – 58/3422
⇒ Profit = 1/3422
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/59, the the profit = 1/3422
∴ When the Cost Price (CP) is 1, then the profit
= 1/3422/1/59
= 1/3422 × 59/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/3422 × 59/1 × 100
= 1 × 59 × 100/3422 × 1
= 5900/3422 = 1.72
Thus, Profit = 1.72% 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 59 articles = $1
And, the Sale Price (SP) of 58 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 59 and 58 = 3422
Now, Let total number of articles purchased = 3422
Here, since the Cost Price of 59 articles = $1
∴ the Cost Price of 1 articles = 1/59
Therefore, the Cost Price of 3422 articles
= 1/59 × 3422⇒ The Cost Price (CP) of 3422 articles = $58And, since the Sale Price of 58 articles = $1
∴ The Sale Price (SP) of 1 article = 1/58
Therefore, the Sale Price of 3422 articles
= 1/58 × 3422 = $59
⇒ The Sale Price (SP) of 3422 articles = $59
Now, the Cost Price (CP) of 3422 articles = $58
And, the Sale Price (SP) of 3422 articles = $59
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)
= 59 – 58 = 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 × 100/58
= 100/58 = 1.72
Thus, profit = 1.72% Answer
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