mcqs Math Profit And Loss If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent. 990

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Question: If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(A)  2.01%
(B)  2.61%
(C)  1.61%
(D)  2.42%

Correct Answer 1.61%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 63 articles = $1

The Sale Price (SP) for 62 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 63 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₃

∵ The Sale Price (SP) for 62 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₂

Calculation of profit

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

= ¹/₆₂ – ¹/₆₃

= ^{63 – 62}/₃₉₀₆

⇒ Profit = ¹/₃₉₀₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₃, the the profit = ¹/₃₉₀₆

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

= ^{¹/₃₉₀₆}/_¹/₆₃

= ¹/₃₉₀₆ × ⁶³/₁

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

= ¹/₃₉₀₆ × ⁶³/₁ × 100

= ^{1 × 63 × 100}/_{3906 × 1}

= ⁶³⁰⁰/₃₉₀₆ = 1.61

Thus, Profit = 1.61% 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 63 articles = $1

And, the Sale Price (SP) of 62 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 63 and 62 = 3906

Now, Let total number of articles purchased = 3906

Here, since the Cost Price of 63 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₃

Therefore, the Cost Price of 3906 articles

= ¹/₆₃ × 3906

⇒ The Cost Price (CP) of 3906 articles = $62

And, since the Sale Price of 62 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₂

Therefore, the Sale Price of 3906 articles

= ¹/₆₂ × 3906 = $63

⇒ The Sale Price (SP) of 3906 articles = $63

Now, the Cost Price (CP) of 3906 articles = $62

And, the Sale Price (SP) of 3906 articles = $63

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)

= 63 – 62 = 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}/₆₂

= ¹⁰⁰/₆₂ = 1.61

Thus, profit = 1.61% Answer