Profit And Loss
Math MCQs

Question :    Calculate the earnings percentage if a vendor buys 56 articles for $1 and sells 55 articles for $1.

Correct Answer  1.82%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 56 articles = $1

The Sale Price (SP) for 55 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 56 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₆

∵ The Sale Price (SP) for 55 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₅

Calculation of profit

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

= ¹/₅₅ – ¹/₅₆

= ^{56 – 55}/₃₀₈₀

⇒ Profit = ¹/₃₀₈₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₆, the the profit = ¹/₃₀₈₀

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

= ^{1/₃₀₈₀}/_¹/56

= ¹/₃₀₈₀ × ⁵⁶/₁

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

= ¹/₃₀₈₀ × ⁵⁶/₁ × 100

= ^{1 × 56 × 100}/_{3080 × 1}

= ⁵⁶⁰⁰/₃₀₈₀ = 1.82

Thus, Profit = 1.82% 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 56 articles = $1

And, the Sale Price (SP) of 55 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 56 and 55 = 3080

Now, Let total number of articles purchased = 3080

Here, since the Cost Price of 56 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₆

Therefore, the Cost Price of 3080 articles

And, since the Sale Price of 55 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₅

Therefore, the Sale Price of 3080 articles

= ¹/₅₅ × 3080 = $56

⇒ The Sale Price (SP) of 3080 articles = $56

Now, the Cost Price (CP) of 3080 articles = $55

And, the Sale Price (SP) of 3080 articles = $56

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)

= 56 – 55 = 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}/₅₅

= ¹⁰⁰/₅₅ = 1.82

Thus, profit = 1.82% Answer

Similar Questions

(1) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.

(2) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?

(3) Find the cost price, if a trader gets a loss of 44% by selling 500 packets of fruits for $48210.60

(4) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(5) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(6) If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

(7) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

(8) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?

(9) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(10) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.