mcqs Math Profit And Loss Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1. 981

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Question: Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

(A)  2.36%
(B)  2.89%
(C)  1.89%
(D)  2.84%

Correct Answer 1.89%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 54 articles = $1

The Sale Price (SP) for 53 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 54 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₄

∵ The Sale Price (SP) for 53 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₃

Calculation of profit

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

= ¹/₅₃ – ¹/₅₄

= ^{54 – 53}/₂₈₆₂

⇒ Profit = ¹/₂₈₆₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₄, the the profit = ¹/₂₈₆₂

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

= ^{¹/₂₈₆₂}/_¹/₅₄

= ¹/₂₈₆₂ × ⁵⁴/₁

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

= ¹/₂₈₆₂ × ⁵⁴/₁ × 100

= ^{1 × 54 × 100}/_{2862 × 1}

= ⁵⁴⁰⁰/₂₈₆₂ = 1.89

Thus, Profit = 1.89% 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 54 articles = $1

And, the Sale Price (SP) of 53 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 54 and 53 = 2862

Now, Let total number of articles purchased = 2862

Here, since the Cost Price of 54 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₄

Therefore, the Cost Price of 2862 articles

= ¹/₅₄ × 2862

⇒ The Cost Price (CP) of 2862 articles = $53

And, since the Sale Price of 53 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₃

Therefore, the Sale Price of 2862 articles

= ¹/₅₃ × 2862 = $54

⇒ The Sale Price (SP) of 2862 articles = $54

Now, the Cost Price (CP) of 2862 articles = $53

And, the Sale Price (SP) of 2862 articles = $54

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)

= 54 – 53 = 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}/₅₃

= ¹⁰⁰/₅₃ = 1.89

Thus, profit = 1.89% Answer