Profit And Loss
Math MCQs

Question :    Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.

Correct Answer  2.38%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 43 articles = $1

The Sale Price (SP) for 42 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 43 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₃

∵ The Sale Price (SP) for 42 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₂

Calculation of profit

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

= ¹/₄₂ – ¹/₄₃

= ^{43 – 42}/₁₈₀₆

⇒ Profit = ¹/₁₈₀₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₃, the the profit = ¹/₁₈₀₆

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

= ^{1/₁₈₀₆}/_¹/43

= ¹/₁₈₀₆ × ⁴³/₁

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

= ¹/₁₈₀₆ × ⁴³/₁ × 100

= ^{1 × 43 × 100}/_{1806 × 1}

= ⁴³⁰⁰/₁₈₀₆ = 2.38

Thus, Profit = 2.38% 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 43 articles = $1

And, the Sale Price (SP) of 42 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 43 and 42 = 1806

Now, Let total number of articles purchased = 1806

Here, since the Cost Price of 43 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₃

Therefore, the Cost Price of 1806 articles

And, since the Sale Price of 42 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₂

Therefore, the Sale Price of 1806 articles

= ¹/₄₂ × 1806 = $43

⇒ The Sale Price (SP) of 1806 articles = $43

Now, the Cost Price (CP) of 1806 articles = $42

And, the Sale Price (SP) of 1806 articles = $43

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)

= 43 – 42 = 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}/₄₂

= ¹⁰⁰/₄₂ = 2.38

Thus, profit = 2.38% Answer

Similar Questions

(1) If a shopkeeper loses 6% by selling some items for $150.40 then, for how much should he sell them to get a profit of 5%?

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

(3) Find the cost price, if a dealer gets a loss of 30% by selling 300 stocks for $4067

(4) Potter loses 90% by selling an article for $436. For how much should he sell it to get a profit of 89%?

(5) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

(6) Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.

(7) 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.

(8) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(9) Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.

(10) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?