mcqs Math Profit And Loss If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent. 959

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Question: If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(A)  4.04%
(B)  4.23%
(C)  3.23%
(D)  4.85%

Correct Answer 3.23%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 32 articles = $1

The Sale Price (SP) for 31 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 32 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₂

∵ The Sale Price (SP) for 31 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₁

Calculation of profit

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

= ¹/₃₁ – ¹/₃₂

= ^{32 – 31}/₉₉₂

⇒ Profit = ¹/₉₉₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₂, the the profit = ¹/₉₉₂

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

= ^¹/₉₉₂/_¹/₃₂

= ¹/₉₉₂ × ³²/₁

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

= ¹/₉₉₂ × ³²/₁ × 100

= ^{1 × 32 × 100}/_{992 × 1}

= ³²⁰⁰/₉₉₂ = 3.23

Thus, Profit = 3.23% 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 32 articles = $1

And, the Sale Price (SP) of 31 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 32 and 31 = 992

Now, Let total number of articles purchased = 992

Here, since the Cost Price of 32 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₂

Therefore, the Cost Price of 992 articles

= ¹/₃₂ × 992

⇒ The Cost Price (CP) of 992 articles = $31

And, since the Sale Price of 31 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₁

Therefore, the Sale Price of 992 articles

= ¹/₃₁ × 992 = $32

⇒ The Sale Price (SP) of 992 articles = $32

Now, the Cost Price (CP) of 992 articles = $31

And, the Sale Price (SP) of 992 articles = $32

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)

= 32 – 31 = 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}/₃₁

= ¹⁰⁰/₃₁ = 3.23

Thus, profit = 3.23% Answer