mcqs Math Profit And Loss How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1? 963

Try MCQ Test

Question: How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?

(A)  3.58%
(B)  3.86%
(C)  2.86%
(D)  4.29%

Correct Answer 2.86%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 36 articles = $1

The Sale Price (SP) for 35 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 36 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₆

∵ The Sale Price (SP) for 35 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₅

Calculation of profit

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

= ¹/₃₅ – ¹/₃₆

= ^{36 – 35}/₁₂₆₀

⇒ Profit = ¹/₁₂₆₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₆, the the profit = ¹/₁₂₆₀

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

= ^{¹/₁₂₆₀}/_¹/₃₆

= ¹/₁₂₆₀ × ³⁶/₁

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

= ¹/₁₂₆₀ × ³⁶/₁ × 100

= ^{1 × 36 × 100}/_{1260 × 1}

= ³⁶⁰⁰/₁₂₆₀ = 2.86

Thus, Profit = 2.86% 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 36 articles = $1

And, the Sale Price (SP) of 35 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 36 and 35 = 1260

Now, Let total number of articles purchased = 1260

Here, since the Cost Price of 36 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₆

Therefore, the Cost Price of 1260 articles

= ¹/₃₆ × 1260

⇒ The Cost Price (CP) of 1260 articles = $35

And, since the Sale Price of 35 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₅

Therefore, the Sale Price of 1260 articles

= ¹/₃₅ × 1260 = $36

⇒ The Sale Price (SP) of 1260 articles = $36

Now, the Cost Price (CP) of 1260 articles = $35

And, the Sale Price (SP) of 1260 articles = $36

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)

= 36 – 35 = 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}/₃₅

= ¹⁰⁰/₃₅ = 2.86

Thus, profit = 2.86% Answer