mcqs Math Profit And Loss A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent? 952

Try MCQ Test

Question: A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(A)  5.21%
(B)  5.17%
(C)  4.17%
(D)  6.26%

Correct Answer 4.17%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 25 articles = $1

The Sale Price (SP) for 24 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 25 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₅

∵ The Sale Price (SP) for 24 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₄

Calculation of profit

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

= ¹/₂₄ – ¹/₂₅

= ^{25 – 24}/₆₀₀

⇒ Profit = ¹/₆₀₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₅, the the profit = ¹/₆₀₀

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

= ^¹/₆₀₀/_¹/₂₅

= ¹/₆₀₀ × ²⁵/₁

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

= ¹/₆₀₀ × ²⁵/₁ × 100

= ^{1 × 25 × 100}/_{600 × 1}

= ²⁵⁰⁰/₆₀₀ = 4.17

Thus, Profit = 4.17% 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 25 articles = $1

And, the Sale Price (SP) of 24 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 25 and 24 = 600

Now, Let total number of articles purchased = 600

Here, since the Cost Price of 25 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₅

Therefore, the Cost Price of 600 articles

= ¹/₂₅ × 600

⇒ The Cost Price (CP) of 600 articles = $24

And, since the Sale Price of 24 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₄

Therefore, the Sale Price of 600 articles

= ¹/₂₄ × 600 = $25

⇒ The Sale Price (SP) of 600 articles = $25

Now, the Cost Price (CP) of 600 articles = $24

And, the Sale Price (SP) of 600 articles = $25

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)

= 25 – 24 = 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}/₂₄

= ¹⁰⁰/₂₄ = 4.17

Thus, profit = 4.17% Answer