Profit And Loss
Math MCQs

Question :    What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

Correct Answer  2.44%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 42 articles = $1

The Sale Price (SP) for 41 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 42 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₂

∵ The Sale Price (SP) for 41 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₁

Calculation of profit

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

= ¹/₄₁ – ¹/₄₂

= ^{42 – 41}/₁₇₂₂

⇒ Profit = ¹/₁₇₂₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₂, the the profit = ¹/₁₇₂₂

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

= ^{1/₁₇₂₂}/_¹/42

= ¹/₁₇₂₂ × ⁴²/₁

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

= ¹/₁₇₂₂ × ⁴²/₁ × 100

= ^{1 × 42 × 100}/_{1722 × 1}

= ⁴²⁰⁰/₁₇₂₂ = 2.44

Thus, Profit = 2.44% 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 42 articles = $1

And, the Sale Price (SP) of 41 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 42 and 41 = 1722

Now, Let total number of articles purchased = 1722

Here, since the Cost Price of 42 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₂

Therefore, the Cost Price of 1722 articles

And, since the Sale Price of 41 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₁

Therefore, the Sale Price of 1722 articles

= ¹/₄₁ × 1722 = $42

⇒ The Sale Price (SP) of 1722 articles = $42

Now, the Cost Price (CP) of 1722 articles = $41

And, the Sale Price (SP) of 1722 articles = $42

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)

= 42 – 41 = 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}/₄₁

= ¹⁰⁰/₄₁ = 2.44

Thus, profit = 2.44% Answer

Similar Questions

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