mcqs Math Profit And Loss A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent? 946

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Question: A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?

(A)  6.95%
(B)  6.56%
(C)  5.56%
(D)  8.34%

Correct Answer 5.56%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 19 articles = $1

The Sale Price (SP) for 18 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 19 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₁₉

∵ The Sale Price (SP) for 18 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₈

Calculation of profit

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

= ¹/₁₈ – ¹/₁₉

= ^{19 – 18}/₃₄₂

⇒ Profit = ¹/₃₄₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₁₉, the the profit = ¹/₃₄₂

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

= ^¹/₃₄₂/_¹/₁₉

= ¹/₃₄₂ × ¹⁹/₁

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

= ¹/₃₄₂ × ¹⁹/₁ × 100

= ^{1 × 19 × 100}/_{342 × 1}

= ¹⁹⁰⁰/₃₄₂ = 5.56

Thus, Profit = 5.56% 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 19 articles = $1

And, the Sale Price (SP) of 18 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 19 and 18 = 342

Now, Let total number of articles purchased = 342

Here, since the Cost Price of 19 articles = $1

∴ the Cost Price of 1 articles = ¹/₁₉

Therefore, the Cost Price of 342 articles

= ¹/₁₉ × 342

⇒ The Cost Price (CP) of 342 articles = $18

And, since the Sale Price of 18 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₈

Therefore, the Sale Price of 342 articles

= ¹/₁₈ × 342 = $19

⇒ The Sale Price (SP) of 342 articles = $19

Now, the Cost Price (CP) of 342 articles = $18

And, the Sale Price (SP) of 342 articles = $19

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)

= 19 – 18 = 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}/₁₈

= ¹⁰⁰/₁₈ = 5.56

Thus, profit = 5.56% Answer