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) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

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

(3) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

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

(5) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(6) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?

(7) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?

(8) Find the cost price, if a trader gets a loss of 38% by selling 600 packets of fruits for $4594.20

(9) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(10) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?