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) William loses 69% by selling an article for $1026.10. For how much should he sell it to get a profit of 68%?

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

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

(4) Find the cost price, if a trader gets a loss of 49% by selling 1500 kg rice for $4901.10

(5) Find the cost price, if a trader gets a loss of 48% by selling 500 kg of rice for $4893.20

(6) Find the cost price, if a trader gets a loss of 50% by selling 500 bags of rice for $4905

(7) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(8) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(9) Find the cost price, if a vendor gets a loss of 15% by selling some articles for $2388.50.

(10) If a dealer loses 61% by selling an article for $1134.90. For how much should he sell it to get a profit of 60%?