Profit And Loss
Math MCQs

Question :    if a vendor bought 74 nibs for $1 and sells them at a rate of 73 per $1 then calculate the profit in percent.

Correct Answer  1.37%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 74 articles = $1

The Sale Price (SP) for 73 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 74 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₄

∵ The Sale Price (SP) for 73 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₃

Calculation of profit

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

= ¹/₇₃ – ¹/₇₄

= ^{74 – 73}/₅₄₀₂

⇒ Profit = ¹/₅₄₀₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₄, the the profit = ¹/₅₄₀₂

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

= ^{1/₅₄₀₂}/_¹/74

= ¹/₅₄₀₂ × ⁷⁴/₁

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

= ¹/₅₄₀₂ × ⁷⁴/₁ × 100

= ^{1 × 74 × 100}/_{5402 × 1}

= ⁷⁴⁰⁰/₅₄₀₂ = 1.37

Thus, Profit = 1.37% 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 74 articles = $1

And, the Sale Price (SP) of 73 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 74 and 73 = 5402

Now, Let total number of articles purchased = 5402

Here, since the Cost Price of 74 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₄

Therefore, the Cost Price of 5402 articles

And, since the Sale Price of 73 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₃

Therefore, the Sale Price of 5402 articles

= ¹/₇₃ × 5402 = $74

⇒ The Sale Price (SP) of 5402 articles = $74

Now, the Cost Price (CP) of 5402 articles = $73

And, the Sale Price (SP) of 5402 articles = $74

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)

= 74 – 73 = 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}/₇₃

= ¹⁰⁰/₇₃ = 1.37

Thus, profit = 1.37% Answer

Similar Questions

(1) William loses 75% by selling an article for $902.50. For how much should he sell it to get a profit of 74%?

(2) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.

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

(4) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(5) After selling some antique items for $6504 a trader earns a profit of 140%. Find the cost price of those antique items.

(6) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(7) What is the cost price if Mrs. Norrah gets a profit of 165% by selling some items for $8506.5

(8) John loses 63% by selling an article for $1113.70. For how much should he sell it to get a profit of 62%?

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

(10) Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??