Profit And Loss
Math MCQs

Question :    Calculate the earnings in percent if a hawker buys 44 articles for $1 and sells 43 articles for $1.

Correct Answer  2.33%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 44 articles = $1

The Sale Price (SP) for 43 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 44 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₄

∵ The Sale Price (SP) for 43 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₃

Calculation of profit

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

= ¹/₄₃ – ¹/₄₄

= ^{44 – 43}/₁₈₉₂

⇒ Profit = ¹/₁₈₉₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₄, the the profit = ¹/₁₈₉₂

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

= ^{1/₁₈₉₂}/_¹/44

= ¹/₁₈₉₂ × ⁴⁴/₁

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

= ¹/₁₈₉₂ × ⁴⁴/₁ × 100

= ^{1 × 44 × 100}/_{1892 × 1}

= ⁴⁴⁰⁰/₁₈₉₂ = 2.33

Thus, Profit = 2.33% 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 44 articles = $1

And, the Sale Price (SP) of 43 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 44 and 43 = 1892

Now, Let total number of articles purchased = 1892

Here, since the Cost Price of 44 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₄

Therefore, the Cost Price of 1892 articles

And, since the Sale Price of 43 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₃

Therefore, the Sale Price of 1892 articles

= ¹/₄₃ × 1892 = $44

⇒ The Sale Price (SP) of 1892 articles = $44

Now, the Cost Price (CP) of 1892 articles = $43

And, the Sale Price (SP) of 1892 articles = $44

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)

= 44 – 43 = 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}/₄₃

= ¹⁰⁰/₄₃ = 2.33

Thus, profit = 2.33% Answer

Similar Questions

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

(2) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

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

(4) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.

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

(6) A shopkeeper gets a loss of 10% by selling an article for $324. For how much should he sell it to get a profit of 9%?

(7) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(8) In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.

(9) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

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