Profit And Loss
Math MCQs

Question :    If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.

Correct Answer  1.39%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 73 articles = $1

The Sale Price (SP) for 72 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 73 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₃

∵ The Sale Price (SP) for 72 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₂

Calculation of profit

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

= ¹/₇₂ – ¹/₇₃

= ^{73 – 72}/₅₂₅₆

⇒ Profit = ¹/₅₂₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₃, the the profit = ¹/₅₂₅₆

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

= ^{1/₅₂₅₆}/_¹/73

= ¹/₅₂₅₆ × ⁷³/₁

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

= ¹/₅₂₅₆ × ⁷³/₁ × 100

= ^{1 × 73 × 100}/_{5256 × 1}

= ⁷³⁰⁰/₅₂₅₆ = 1.39

Thus, Profit = 1.39% 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 73 articles = $1

And, the Sale Price (SP) of 72 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 73 and 72 = 5256

Now, Let total number of articles purchased = 5256

Here, since the Cost Price of 73 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₃

Therefore, the Cost Price of 5256 articles

And, since the Sale Price of 72 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₂

Therefore, the Sale Price of 5256 articles

= ¹/₇₂ × 5256 = $73

⇒ The Sale Price (SP) of 5256 articles = $73

Now, the Cost Price (CP) of 5256 articles = $72

And, the Sale Price (SP) of 5256 articles = $73

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)

= 73 – 72 = 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}/₇₂

= ¹⁰⁰/₇₂ = 1.39

Thus, profit = 1.39% Answer

Similar Questions

(1) Find the cost price, if Mrs. Mary earns a profit of 270% by selling some articles for $19647

(2) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

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

(4) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(5) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

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

(7) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(8) 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%?

(9) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(10) If a trader gets a loss of 14% by selling some articles for $2244.60 then what was his cost price?