mcqs Math Profit And Loss If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling. 995

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Question: If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

(A)  1.86%
(B)  2.49%
(C)  1.49%
(D)  2.24%

Correct Answer 1.49%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 68 articles = $1

The Sale Price (SP) for 67 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 68 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₈

∵ The Sale Price (SP) for 67 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₇

Calculation of profit

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

= ¹/₆₇ – ¹/₆₈

= ^{68 – 67}/₄₅₅₆

⇒ Profit = ¹/₄₅₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₈, the the profit = ¹/₄₅₅₆

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

= ^{¹/₄₅₅₆}/_¹/₆₈

= ¹/₄₅₅₆ × ⁶⁸/₁

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

= ¹/₄₅₅₆ × ⁶⁸/₁ × 100

= ^{1 × 68 × 100}/_{4556 × 1}

= ⁶⁸⁰⁰/₄₅₅₆ = 1.49

Thus, Profit = 1.49% 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 68 articles = $1

And, the Sale Price (SP) of 67 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 68 and 67 = 4556

Now, Let total number of articles purchased = 4556

Here, since the Cost Price of 68 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₈

Therefore, the Cost Price of 4556 articles

= ¹/₆₈ × 4556

⇒ The Cost Price (CP) of 4556 articles = $67

And, since the Sale Price of 67 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₇

Therefore, the Sale Price of 4556 articles

= ¹/₆₇ × 4556 = $68

⇒ The Sale Price (SP) of 4556 articles = $68

Now, the Cost Price (CP) of 4556 articles = $67

And, the Sale Price (SP) of 4556 articles = $68

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)

= 68 – 67 = 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}/₆₇

= ¹⁰⁰/₆₇ = 1.49

Thus, profit = 1.49% Answer