mcqs Math Profit And Loss A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent. 974

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Question: A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent.

(A)  2.71%
(B)  3.17%
(C)  2.17%
(D)  3.26%

Correct Answer 2.17%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 47 articles = $1

The Sale Price (SP) for 46 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 47 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₇

∵ The Sale Price (SP) for 46 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₆

Calculation of profit

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

= ¹/₄₆ – ¹/₄₇

= ^{47 – 46}/₂₁₆₂

⇒ Profit = ¹/₂₁₆₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₇, the the profit = ¹/₂₁₆₂

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

= ^{¹/₂₁₆₂}/_¹/₄₇

= ¹/₂₁₆₂ × ⁴⁷/₁

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

= ¹/₂₁₆₂ × ⁴⁷/₁ × 100

= ^{1 × 47 × 100}/_{2162 × 1}

= ⁴⁷⁰⁰/₂₁₆₂ = 2.17

Thus, Profit = 2.17% 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 47 articles = $1

And, the Sale Price (SP) of 46 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 47 and 46 = 2162

Now, Let total number of articles purchased = 2162

Here, since the Cost Price of 47 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₇

Therefore, the Cost Price of 2162 articles

= ¹/₄₇ × 2162

⇒ The Cost Price (CP) of 2162 articles = $46

And, since the Sale Price of 46 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₆

Therefore, the Sale Price of 2162 articles

= ¹/₄₆ × 2162 = $47

⇒ The Sale Price (SP) of 2162 articles = $47

Now, the Cost Price (CP) of 2162 articles = $46

And, the Sale Price (SP) of 2162 articles = $47

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)

= 47 – 46 = 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}/₄₆

= ¹⁰⁰/₄₆ = 2.17

Thus, profit = 2.17% Answer