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 33% by selling an article for $1011.70. For how much should he sell it to get a profit of 32%?

(2) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(3) A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

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

(5) Find the cost price, if Mr. Jojo earns a profit of 355% by selling some articles for $31895.5

(6) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(7) If Rohilla sold his furniture for $663 at a profit of 30%, then for how much he had purchased them?

(8) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

(9) Peter loses 3% by selling an article for $9.70. For how much should he sell it to get a profit of 2%?

(10) Find the cost price, if a dealer earns a profit of 245% by selling a plot for $16594.5