mcqs Math Profit And Loss If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent. 989

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Question: If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

(A)  2.05%
(B)  2.64%
(C)  1.64%
(D)  2.46%

Correct Answer 1.64%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 62 articles = $1

The Sale Price (SP) for 61 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 62 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₂

∵ The Sale Price (SP) for 61 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₁

Calculation of profit

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

= ¹/₆₁ – ¹/₆₂

= ^{62 – 61}/₃₇₈₂

⇒ Profit = ¹/₃₇₈₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₂, the the profit = ¹/₃₇₈₂

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

= ^{¹/₃₇₈₂}/_¹/₆₂

= ¹/₃₇₈₂ × ⁶²/₁

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

= ¹/₃₇₈₂ × ⁶²/₁ × 100

= ^{1 × 62 × 100}/_{3782 × 1}

= ⁶²⁰⁰/₃₇₈₂ = 1.64

Thus, Profit = 1.64% 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 62 articles = $1

And, the Sale Price (SP) of 61 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 62 and 61 = 3782

Now, Let total number of articles purchased = 3782

Here, since the Cost Price of 62 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₂

Therefore, the Cost Price of 3782 articles

= ¹/₆₂ × 3782

⇒ The Cost Price (CP) of 3782 articles = $61

And, since the Sale Price of 61 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₁

Therefore, the Sale Price of 3782 articles

= ¹/₆₁ × 3782 = $62

⇒ The Sale Price (SP) of 3782 articles = $62

Now, the Cost Price (CP) of 3782 articles = $61

And, the Sale Price (SP) of 3782 articles = $62

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)

= 62 – 61 = 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}/₆₁

= ¹⁰⁰/₆₁ = 1.64

Thus, profit = 1.64% Answer