mcqs Math Profit And Loss If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be? 947

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Question: If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(A)  6.58%
(B)  6.26%
(C)  5.26%
(D)  7.89%

Correct Answer 5.26%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 20 articles = $1

The Sale Price (SP) for 19 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 20 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₀

∵ The Sale Price (SP) for 19 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₉

Calculation of profit

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

= ¹/₁₉ – ¹/₂₀

= ^{20 – 19}/₃₈₀

⇒ Profit = ¹/₃₈₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₀, the the profit = ¹/₃₈₀

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

= ^¹/₃₈₀/_¹/₂₀

= ¹/₃₈₀ × ²⁰/₁

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

= ¹/₃₈₀ × ²⁰/₁ × 100

= ^{1 × 20 × 100}/_{380 × 1}

= ²⁰⁰⁰/₃₈₀ = 5.26

Thus, Profit = 5.26% 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 20 articles = $1

And, the Sale Price (SP) of 19 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 20 and 19 = 380

Now, Let total number of articles purchased = 380

Here, since the Cost Price of 20 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₀

Therefore, the Cost Price of 380 articles

= ¹/₂₀ × 380

⇒ The Cost Price (CP) of 380 articles = $19

And, since the Sale Price of 19 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₉

Therefore, the Sale Price of 380 articles

= ¹/₁₉ × 380 = $20

⇒ The Sale Price (SP) of 380 articles = $20

Now, the Cost Price (CP) of 380 articles = $19

And, the Sale Price (SP) of 380 articles = $20

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)

= 20 – 19 = 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}/₁₉

= ¹⁰⁰/₁₉ = 5.26

Thus, profit = 5.26% Answer