mcqs Math Profit And Loss if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent. 1001

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Question: if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

(A)  1.71%
(B)  2.37%
(C)  1.37%
(D)  2.06%

Correct Answer 1.37%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 74 articles = $1

The Sale Price (SP) for 73 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 74 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₄

∵ The Sale Price (SP) for 73 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₃

Calculation of profit

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

= ¹/₇₃ – ¹/₇₄

= ^{74 – 73}/₅₄₀₂

⇒ Profit = ¹/₅₄₀₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₄, the the profit = ¹/₅₄₀₂

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

= ^{¹/₅₄₀₂}/_¹/₇₄

= ¹/₅₄₀₂ × ⁷⁴/₁

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

= ¹/₅₄₀₂ × ⁷⁴/₁ × 100

= ^{1 × 74 × 100}/_{5402 × 1}

= ⁷⁴⁰⁰/₅₄₀₂ = 1.37

Thus, Profit = 1.37% 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 74 articles = $1

And, the Sale Price (SP) of 73 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 74 and 73 = 5402

Now, Let total number of articles purchased = 5402

Here, since the Cost Price of 74 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₄

Therefore, the Cost Price of 5402 articles

= ¹/₇₄ × 5402

⇒ The Cost Price (CP) of 5402 articles = $73

And, since the Sale Price of 73 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₃

Therefore, the Sale Price of 5402 articles

= ¹/₇₃ × 5402 = $74

⇒ The Sale Price (SP) of 5402 articles = $74

Now, the Cost Price (CP) of 5402 articles = $73

And, the Sale Price (SP) of 5402 articles = $74

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)

= 74 – 73 = 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}/₇₃

= ¹⁰⁰/₇₃ = 1.37

Thus, profit = 1.37% Answer