Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.

Correct Answer  1.92%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 53 articles = $1

The Sale Price (SP) for 52 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 53 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₃

∵ The Sale Price (SP) for 52 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₂

Calculation of profit

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

= ¹/₅₂ – ¹/₅₃

= ^{53 – 52}/₂₇₅₆

⇒ Profit = ¹/₂₇₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₃, the the profit = ¹/₂₇₅₆

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

= ^{1/₂₇₅₆}/_¹/53

= ¹/₂₇₅₆ × ⁵³/₁

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

= ¹/₂₇₅₆ × ⁵³/₁ × 100

= ^{1 × 53 × 100}/_{2756 × 1}

= ⁵³⁰⁰/₂₇₅₆ = 1.92

Thus, Profit = 1.92% 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 53 articles = $1

And, the Sale Price (SP) of 52 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 53 and 52 = 2756

Now, Let total number of articles purchased = 2756

Here, since the Cost Price of 53 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₃

Therefore, the Cost Price of 2756 articles

And, since the Sale Price of 52 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₂

Therefore, the Sale Price of 2756 articles

= ¹/₅₂ × 2756 = $53

⇒ The Sale Price (SP) of 2756 articles = $53

Now, the Cost Price (CP) of 2756 articles = $52

And, the Sale Price (SP) of 2756 articles = $53

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)

= 53 – 52 = 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}/₅₂

= ¹⁰⁰/₅₂ = 1.92

Thus, profit = 1.92% Answer

Similar Questions

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

(2) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(3) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(4) Potter loses 89% by selling an article for $474.10. For how much should he sell it to get a profit of 88%?

(5) A trader earns a profit of 205% by selling some articles for $12230.50. What was the cost price?

(6) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?

(7) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(8) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(9) Find the cost price, if a trader gets a loss of 62% by selling 10 TV sets for $4639.80

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