mcqs Math Profit And Loss Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1. 994

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Question: Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.

(A)  1.9%
(B)  2.52%
(C)  1.52%
(D)  2.28%

Correct Answer 1.52%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 67 articles = $1

The Sale Price (SP) for 66 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 67 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₇

∵ The Sale Price (SP) for 66 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₆

Calculation of profit

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

= ¹/₆₆ – ¹/₆₇

= ^{67 – 66}/₄₄₂₂

⇒ Profit = ¹/₄₄₂₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₇, the the profit = ¹/₄₄₂₂

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

= ^{¹/₄₄₂₂}/_¹/₆₇

= ¹/₄₄₂₂ × ⁶⁷/₁

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

= ¹/₄₄₂₂ × ⁶⁷/₁ × 100

= ^{1 × 67 × 100}/_{4422 × 1}

= ⁶⁷⁰⁰/₄₄₂₂ = 1.52

Thus, Profit = 1.52% 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 67 articles = $1

And, the Sale Price (SP) of 66 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 67 and 66 = 4422

Now, Let total number of articles purchased = 4422

Here, since the Cost Price of 67 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₇

Therefore, the Cost Price of 4422 articles

= ¹/₆₇ × 4422

⇒ The Cost Price (CP) of 4422 articles = $66

And, since the Sale Price of 66 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₆

Therefore, the Sale Price of 4422 articles

= ¹/₆₆ × 4422 = $67

⇒ The Sale Price (SP) of 4422 articles = $67

Now, the Cost Price (CP) of 4422 articles = $66

And, the Sale Price (SP) of 4422 articles = $67

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)

= 67 – 66 = 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}/₆₆

= ¹⁰⁰/₆₆ = 1.52

Thus, profit = 1.52% Answer