mcqs Math Profit And Loss What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1? 997

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Question: What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(A)  1.81%
(B)  2.45%
(C)  1.45%
(D)  2.18%

Correct Answer 1.45%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 70 articles = $1

The Sale Price (SP) for 69 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 70 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₀

∵ The Sale Price (SP) for 69 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₉

Calculation of profit

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

= ¹/₆₉ – ¹/₇₀

= ^{70 – 69}/₄₈₃₀

⇒ Profit = ¹/₄₈₃₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₀, the the profit = ¹/₄₈₃₀

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

= ^{¹/₄₈₃₀}/_¹/₇₀

= ¹/₄₈₃₀ × ⁷⁰/₁

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

= ¹/₄₈₃₀ × ⁷⁰/₁ × 100

= ^{1 × 70 × 100}/_{4830 × 1}

= ⁷⁰⁰⁰/₄₈₃₀ = 1.45

Thus, Profit = 1.45% 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 70 articles = $1

And, the Sale Price (SP) of 69 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 70 and 69 = 4830

Now, Let total number of articles purchased = 4830

Here, since the Cost Price of 70 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₀

Therefore, the Cost Price of 4830 articles

= ¹/₇₀ × 4830

⇒ The Cost Price (CP) of 4830 articles = $69

And, since the Sale Price of 69 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₉

Therefore, the Sale Price of 4830 articles

= ¹/₆₉ × 4830 = $70

⇒ The Sale Price (SP) of 4830 articles = $70

Now, the Cost Price (CP) of 4830 articles = $69

And, the Sale Price (SP) of 4830 articles = $70

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)

= 70 – 69 = 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}/₆₉

= ¹⁰⁰/₆₉ = 1.45

Thus, profit = 1.45% Answer