mcqs Math Profit And Loss Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent. 958

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Question: Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

(A)  4.16%
(B)  4.33%
(C)  3.33%
(D)  5%

Correct Answer 3.33%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 31 articles = $1

The Sale Price (SP) for 30 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 31 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₁

∵ The Sale Price (SP) for 30 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₀

Calculation of profit

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

= ¹/₃₀ – ¹/₃₁

= ^{31 – 30}/₉₃₀

⇒ Profit = ¹/₉₃₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₁, the the profit = ¹/₉₃₀

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

= ^¹/₉₃₀/_¹/₃₁

= ¹/₉₃₀ × ³¹/₁

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

= ¹/₉₃₀ × ³¹/₁ × 100

= ^{1 × 31 × 100}/_{930 × 1}

= ³¹⁰⁰/₉₃₀ = 3.33

Thus, Profit = 3.33% 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 31 articles = $1

And, the Sale Price (SP) of 30 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 31 and 30 = 930

Now, Let total number of articles purchased = 930

Here, since the Cost Price of 31 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₁

Therefore, the Cost Price of 930 articles

= ¹/₃₁ × 930

⇒ The Cost Price (CP) of 930 articles = $30

And, since the Sale Price of 30 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₀

Therefore, the Sale Price of 930 articles

= ¹/₃₀ × 930 = $31

⇒ The Sale Price (SP) of 930 articles = $31

Now, the Cost Price (CP) of 930 articles = $30

And, the Sale Price (SP) of 930 articles = $31

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)

= 31 – 30 = 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}/₃₀

= ¹⁰⁰/₃₀ = 3.33

Thus, profit = 3.33% Answer