Profit And Loss
Math MCQs

Question :    Calculate the earnings percentage if a vendor buys 54 articles for $1 and sells 53 articles for $1.

Correct Answer  1.89%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 54 articles = $1

The Sale Price (SP) for 53 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 54 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₄

∵ The Sale Price (SP) for 53 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₃

Calculation of profit

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

= ¹/₅₃ – ¹/₅₄

= ^{54 – 53}/₂₈₆₂

⇒ Profit = ¹/₂₈₆₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₄, the the profit = ¹/₂₈₆₂

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

= ^{1/₂₈₆₂}/_¹/54

= ¹/₂₈₆₂ × ⁵⁴/₁

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

= ¹/₂₈₆₂ × ⁵⁴/₁ × 100

= ^{1 × 54 × 100}/_{2862 × 1}

= ⁵⁴⁰⁰/₂₈₆₂ = 1.89

Thus, Profit = 1.89% 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 54 articles = $1

And, the Sale Price (SP) of 53 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 54 and 53 = 2862

Now, Let total number of articles purchased = 2862

Here, since the Cost Price of 54 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₄

Therefore, the Cost Price of 2862 articles

And, since the Sale Price of 53 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₃

Therefore, the Sale Price of 2862 articles

= ¹/₅₃ × 2862 = $54

⇒ The Sale Price (SP) of 2862 articles = $54

Now, the Cost Price (CP) of 2862 articles = $53

And, the Sale Price (SP) of 2862 articles = $54

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)

= 54 – 53 = 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}/₅₃

= ¹⁰⁰/₅₃ = 1.89

Thus, profit = 1.89% Answer

Similar Questions

(1) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.

(2) If a dealer gets a loss of 75% by selling 200 boxes of apple for $3702.50 then find the cost price.

(3) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?

(4) If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

(5) Mr. Bob gets a loss of 11% after selling an article for $364.90. For how much would he sell it to get a profit of 10%?

(6) A street seller buys 8 articles for $1 and sells 7 articles for $1. Find the profit percent in this sale.

(7) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

(8) Find the cost price, if a trader gets a loss of 42% by selling an article for $4761.80

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

(10) Find the cost price, if a trader gets a loss of 60% by selling five TV sets for $4724