mcqs Math Profit And Loss If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage. 1002

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Question: If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage.

(A)  1.69%
(B)  2.35%
(C)  1.35%
(D)  2.03%

Correct Answer 1.35%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 75 articles = $1

The Sale Price (SP) for 74 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 75 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₅

∵ The Sale Price (SP) for 74 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₄

Calculation of profit

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

= ¹/₇₄ – ¹/₇₅

= ^{75 – 74}/₅₅₅₀

⇒ Profit = ¹/₅₅₅₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₅, the the profit = ¹/₅₅₅₀

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

= ^{¹/₅₅₅₀}/_¹/₇₅

= ¹/₅₅₅₀ × ⁷⁵/₁

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

= ¹/₅₅₅₀ × ⁷⁵/₁ × 100

= ^{1 × 75 × 100}/_{5550 × 1}

= ⁷⁵⁰⁰/₅₅₅₀ = 1.35

Thus, Profit = 1.35% 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 75 articles = $1

And, the Sale Price (SP) of 74 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 75 and 74 = 5550

Now, Let total number of articles purchased = 5550

Here, since the Cost Price of 75 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₅

Therefore, the Cost Price of 5550 articles

= ¹/₇₅ × 5550

⇒ The Cost Price (CP) of 5550 articles = $74

And, since the Sale Price of 74 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₄

Therefore, the Sale Price of 5550 articles

= ¹/₇₄ × 5550 = $75

⇒ The Sale Price (SP) of 5550 articles = $75

Now, the Cost Price (CP) of 5550 articles = $74

And, the Sale Price (SP) of 5550 articles = $75

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)

= 75 – 74 = 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}/₇₄

= ¹⁰⁰/₇₄ = 1.35

Thus, profit = 1.35% Answer