mcqs Math Profit And Loss What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1? 1003

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Question: What will be thr profit in percent if a vendor purchased 76 pins for $1 and sold 75 pins for $1?

(A)  1.66%
(B)  2.33%
(C)  1.33%
(D)  2%

Correct Answer 1.33%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 76 articles = $1

The Sale Price (SP) for 75 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 76 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₆

∵ The Sale Price (SP) for 75 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₅

Calculation of profit

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

= ¹/₇₅ – ¹/₇₆

= ^{76 – 75}/₅₇₀₀

⇒ Profit = ¹/₅₇₀₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₆, the the profit = ¹/₅₇₀₀

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

= ^{¹/₅₇₀₀}/_¹/₇₆

= ¹/₅₇₀₀ × ⁷⁶/₁

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

= ¹/₅₇₀₀ × ⁷⁶/₁ × 100

= ^{1 × 76 × 100}/_{5700 × 1}

= ⁷⁶⁰⁰/₅₇₀₀ = 1.33

Thus, Profit = 1.33% 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 76 articles = $1

And, the Sale Price (SP) of 75 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 76 and 75 = 5700

Now, Let total number of articles purchased = 5700

Here, since the Cost Price of 76 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₆

Therefore, the Cost Price of 5700 articles

= ¹/₇₆ × 5700

⇒ The Cost Price (CP) of 5700 articles = $75

And, since the Sale Price of 75 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₅

Therefore, the Sale Price of 5700 articles

= ¹/₇₅ × 5700 = $76

⇒ The Sale Price (SP) of 5700 articles = $76

Now, the Cost Price (CP) of 5700 articles = $75

And, the Sale Price (SP) of 5700 articles = $76

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)

= 76 – 75 = 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}/₇₅

= ¹⁰⁰/₇₅ = 1.33

Thus, profit = 1.33% Answer