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) A shopkeeper loses 51% by selling an article for $1180.90. For how much should he sell it to get a profit of 50%?

(2) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?

(3) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(4) Potter loses 91% by selling an article for $396.90. For how much should he sell it to get a profit of 90%?

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

(6) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(7) A seller gets a profit of 7% by selling a TV set for $4280. If he would have sold it for $4200, then find his profit percent.

(8) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(9) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(10) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.