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) Mr. Steven loses 92% by selling an article for $356.80. For how much should he sell it to get a profit of 91%?

(2) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?

(3) What will be the profit in percent if a vendor buys 70 paper clips for $1 and sells at a rate of 69 per $1?

(4) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(5) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

(6) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.

(7) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.

(8) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(9) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(10) Mr. Oliver loses 80% by selling an article for $772.00. For how much should he sell it to get a profit of 79%?