Question:
Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.
Correct Answer
1.96%
Solution And Explanation
Solution
Given,
The Cost Price (CP) for 52 articles = $1
The Sale Price (SP) for 51 articles = $1
Thus, Profit percent = ?
Unitary Method to find the profit when Cost Price and Sale Price are given
∵ The Cost Price (CP) for 52 articles = $1
Therefore, the Cost Price (CP) for 1 lemon = 1/52
∵ The Sale Price (SP) for 51 articles = $1
Therefore, the Sale Price (SP) for 1 lemon = 1/51
Calculation of profit
Profit = Sale Price (SP) – Cost Price (CP)
= 1/51 – 1/52
= 52 – 51/2652
⇒ Profit = 1/2652
Calculation of Profit Percent using Unitary Method
∵ When the Cost Price (CP) is 1/52, the the profit = 1/2652
∴ When the Cost Price (CP) is 1, then the profit
= 1/2652/1/52
= 1/2652 × 52/1
∴ When the Cost Price (CP) is 100, then the profit
= 1/2652 × 52/1 × 100
= 1 × 52 × 100/2652 × 1
= 5200/2652 = 1.96
Thus, Profit = 1.96% 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 52 articles = $1
And, the Sale Price (SP) of 51 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 52 and 51 = 2652
Now, Let total number of articles purchased = 2652
Here, since the Cost Price of 52 articles = $1
∴ the Cost Price of 1 articles = 1/52
Therefore, the Cost Price of 2652 articles
= 1/52 × 2652⇒ The Cost Price (CP) of 2652 articles = $51And, since the Sale Price of 51 articles = $1
∴ The Sale Price (SP) of 1 article = 1/51
Therefore, the Sale Price of 2652 articles
= 1/51 × 2652 = $52
⇒ The Sale Price (SP) of 2652 articles = $52
Now, the Cost Price (CP) of 2652 articles = $51
And, the Sale Price (SP) of 2652 articles = $52
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)
= 52 – 51 = 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 × 100/51
= 100/51 = 1.96
Thus, profit = 1.96% Answer
Similar Questions
(1) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?
(2) Mrs. Jolly loses 18% by selling an article for $623.20. For how much should she sell it to get a profit of 17%?
(3) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.
(4) Mike sold his car at a profit of 25%. If he purchased that car at $2500 then find the sale price of the car.
(5) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?
(6) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?
(7) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647
(8) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?
(9) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.
(10) A shopkeeper gets a loss of 5% by selling some fruits for $769.50. Find the cost price of the furits.