Profit And Loss
Math MCQs

Question :    Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.

Correct Answer  1.79%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 57 articles = $1

The Sale Price (SP) for 56 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 57 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₇

∵ The Sale Price (SP) for 56 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₆

Calculation of profit

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

= ¹/₅₆ – ¹/₅₇

= ^{57 – 56}/₃₁₉₂

⇒ Profit = ¹/₃₁₉₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₇, the the profit = ¹/₃₁₉₂

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

= ^{1/₃₁₉₂}/_¹/57

= ¹/₃₁₉₂ × ⁵⁷/₁

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

= ¹/₃₁₉₂ × ⁵⁷/₁ × 100

= ^{1 × 57 × 100}/_{3192 × 1}

= ⁵⁷⁰⁰/₃₁₉₂ = 1.79

Thus, Profit = 1.79% 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 57 articles = $1

And, the Sale Price (SP) of 56 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 57 and 56 = 3192

Now, Let total number of articles purchased = 3192

Here, since the Cost Price of 57 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₇

Therefore, the Cost Price of 3192 articles

And, since the Sale Price of 56 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₆

Therefore, the Sale Price of 3192 articles

= ¹/₅₆ × 3192 = $57

⇒ The Sale Price (SP) of 3192 articles = $57

Now, the Cost Price (CP) of 3192 articles = $56

And, the Sale Price (SP) of 3192 articles = $57

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)

= 57 – 56 = 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}/₅₆

= ¹⁰⁰/₅₆ = 1.79

Thus, profit = 1.79% Answer

Similar Questions

(1) Find the profit percent if a vendor buys 9 articles for $1 and sells 8 articles for $1.

(2) Calculate the profit in percent if Mr. John buys 67 articles for $1 and sells 66 articles for $1.

(3) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5

(4) A dealer loses 23% by selling an article for $777.7. For how much should he sell it to get a profit of 22%?

(5) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

(6) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(7) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(8) If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

(9) Find the cost price, if a trader earns a profit of 265% by selling an article for $19016.5

(10) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.