mcqs Math Profit And Loss Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1. 983

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Question: Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.

(A)  2.28%
(B)  2.82%
(C)  1.82%
(D)  2.73%

Correct Answer 1.82%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 56 articles = $1

The Sale Price (SP) for 55 articles = $1

Thus, Profit percent = ?

Unitary Method to find the profit when Cost Price and Sale Price are given

∵ The Cost Price (CP) for 56 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₆

∵ The Sale Price (SP) for 55 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₅

Calculation of profit

Profit = Sale Price (SP) – Cost Price (CP)

= ¹/₅₅ – ¹/₅₆

= ^{56 – 55}/₃₀₈₀

⇒ Profit = ¹/₃₀₈₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₆, the the profit = ¹/₃₀₈₀

∴ When the Cost Price (CP) is 1, then the profit

= ^{¹/₃₀₈₀}/_¹/₅₆

= ¹/₃₀₈₀ × ⁵⁶/₁

∴ When the Cost Price (CP) is 100, then the profit

= ¹/₃₀₈₀ × ⁵⁶/₁ × 100

= ^{1 × 56 × 100}/_{3080 × 1}

= ⁵⁶⁰⁰/₃₀₈₀ = 1.82

Thus, Profit = 1.82% 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 56 articles = $1

And, the Sale Price (SP) of 55 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 56 and 55 = 3080

Now, Let total number of articles purchased = 3080

Here, since the Cost Price of 56 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₆

Therefore, the Cost Price of 3080 articles

= ¹/₅₆ × 3080

⇒ The Cost Price (CP) of 3080 articles = $55

And, since the Sale Price of 55 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₅

Therefore, the Sale Price of 3080 articles

= ¹/₅₅ × 3080 = $56

⇒ The Sale Price (SP) of 3080 articles = $56

Now, the Cost Price (CP) of 3080 articles = $55

And, the Sale Price (SP) of 3080 articles = $56

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)

= 56 – 55 = 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}/₅₅

= ¹⁰⁰/₅₅ = 1.82

Thus, profit = 1.82% Answer