Profit And Loss
Math MCQs

Question :    How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

Correct Answer  2.63%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 39 articles = $1

The Sale Price (SP) for 38 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 39 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₉

∵ The Sale Price (SP) for 38 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₈

Calculation of profit

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

= ¹/₃₈ – ¹/₃₉

= ^{39 – 38}/₁₄₈₂

⇒ Profit = ¹/₁₄₈₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₉, the the profit = ¹/₁₄₈₂

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

= ^{1/₁₄₈₂}/_¹/39

= ¹/₁₄₈₂ × ³⁹/₁

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

= ¹/₁₄₈₂ × ³⁹/₁ × 100

= ^{1 × 39 × 100}/_{1482 × 1}

= ³⁹⁰⁰/₁₄₈₂ = 2.63

Thus, Profit = 2.63% 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 39 articles = $1

And, the Sale Price (SP) of 38 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 39 and 38 = 1482

Now, Let total number of articles purchased = 1482

Here, since the Cost Price of 39 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₉

Therefore, the Cost Price of 1482 articles

And, since the Sale Price of 38 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₈

Therefore, the Sale Price of 1482 articles

= ¹/₃₈ × 1482 = $39

⇒ The Sale Price (SP) of 1482 articles = $39

Now, the Cost Price (CP) of 1482 articles = $38

And, the Sale Price (SP) of 1482 articles = $39

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)

= 39 – 38 = 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}/₃₈

= ¹⁰⁰/₃₈ = 2.63

Thus, profit = 2.63% Answer

Similar Questions

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(2) Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

(3) Find the cost price, if a trader gets a loss of 64% by selling five TV sets for $4539.6

(4) Find the profit percent if Mrs. Julie buys 29 bananas for $1 and sells 28 bananas for $1.

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(6) Find the cost price, if a trader gets a loss of 59% by selling five TV sets for $4760.10

(7) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(8) Find the cost price, if a trader gets a loss of 1% by selling an article for $9.9

(9) What will be the cost price if a shopkeeper sells some clothes for $994 and earns a profit of 40%?

(10) Find the cost price, if a trader gets a loss of 61% by selling 4 TV sets for $4683.90