mcqs Math Profit And Loss If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent. 988

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Question: If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(A)  2.09%
(B)  2.67%
(C)  1.67%
(D)  2.51%

Correct Answer 1.67%

Solution And Explanation

Solution

Given,

The Cost Price (CP) for 61 articles = $1

The Sale Price (SP) for 60 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 61 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₁

∵ The Sale Price (SP) for 60 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₀

Calculation of profit

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

= ¹/₆₀ – ¹/₆₁

= ^{61 – 60}/₃₆₆₀

⇒ Profit = ¹/₃₆₆₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₁, the the profit = ¹/₃₆₆₀

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

= ^{¹/₃₆₆₀}/_¹/₆₁

= ¹/₃₆₆₀ × ⁶¹/₁

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

= ¹/₃₆₆₀ × ⁶¹/₁ × 100

= ^{1 × 61 × 100}/_{3660 × 1}

= ⁶¹⁰⁰/₃₆₆₀ = 1.67

Thus, Profit = 1.67% 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 61 articles = $1

And, the Sale Price (SP) of 60 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 61 and 60 = 3660

Now, Let total number of articles purchased = 3660

Here, since the Cost Price of 61 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₁

Therefore, the Cost Price of 3660 articles

= ¹/₆₁ × 3660

⇒ The Cost Price (CP) of 3660 articles = $60

And, since the Sale Price of 60 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₀

Therefore, the Sale Price of 3660 articles

= ¹/₆₀ × 3660 = $61

⇒ The Sale Price (SP) of 3660 articles = $61

Now, the Cost Price (CP) of 3660 articles = $60

And, the Sale Price (SP) of 3660 articles = $61

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)

= 61 – 60 = 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}/₆₀

= ¹⁰⁰/₆₀ = 1.67

Thus, profit = 1.67% Answer