mcqs Math Profit And Loss If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent. 1000

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Question: If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.

(A)  1.74%
(B)  2.39%
(C)  1.39%
(D)  2.09%

Correct Answer 1.39%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 73 articles = $1

The Sale Price (SP) for 72 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 73 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₃

∵ The Sale Price (SP) for 72 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₂

Calculation of profit

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

= ¹/₇₂ – ¹/₇₃

= ^{73 – 72}/₅₂₅₆

⇒ Profit = ¹/₅₂₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₃, the the profit = ¹/₅₂₅₆

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

= ^{¹/₅₂₅₆}/_¹/₇₃

= ¹/₅₂₅₆ × ⁷³/₁

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

= ¹/₅₂₅₆ × ⁷³/₁ × 100

= ^{1 × 73 × 100}/_{5256 × 1}

= ⁷³⁰⁰/₅₂₅₆ = 1.39

Thus, Profit = 1.39% 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 73 articles = $1

And, the Sale Price (SP) of 72 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 73 and 72 = 5256

Now, Let total number of articles purchased = 5256

Here, since the Cost Price of 73 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₃

Therefore, the Cost Price of 5256 articles

= ¹/₇₃ × 5256

⇒ The Cost Price (CP) of 5256 articles = $72

And, since the Sale Price of 72 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₂

Therefore, the Sale Price of 5256 articles

= ¹/₇₂ × 5256 = $73

⇒ The Sale Price (SP) of 5256 articles = $73

Now, the Cost Price (CP) of 5256 articles = $72

And, the Sale Price (SP) of 5256 articles = $73

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)

= 73 – 72 = 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}/₇₂

= ¹⁰⁰/₇₂ = 1.39

Thus, profit = 1.39% Answer