Profit And Loss
Math MCQs

Question :    Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

Correct Answer  1.41%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 72 articles = $1

The Sale Price (SP) for 71 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 72 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₇₂

∵ The Sale Price (SP) for 71 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₇₁

Calculation of profit

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

= ¹/₇₁ – ¹/₇₂

= ^{72 – 71}/₅₁₁₂

⇒ Profit = ¹/₅₁₁₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₇₂, the the profit = ¹/₅₁₁₂

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

= ^{1/₅₁₁₂}/_¹/72

= ¹/₅₁₁₂ × ⁷²/₁

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

= ¹/₅₁₁₂ × ⁷²/₁ × 100

= ^{1 × 72 × 100}/_{5112 × 1}

= ⁷²⁰⁰/₅₁₁₂ = 1.41

Thus, Profit = 1.41% 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 72 articles = $1

And, the Sale Price (SP) of 71 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 72 and 71 = 5112

Now, Let total number of articles purchased = 5112

Here, since the Cost Price of 72 articles = $1

∴ the Cost Price of 1 articles = ¹/₇₂

Therefore, the Cost Price of 5112 articles

And, since the Sale Price of 71 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₇₁

Therefore, the Sale Price of 5112 articles

= ¹/₇₁ × 5112 = $72

⇒ The Sale Price (SP) of 5112 articles = $72

Now, the Cost Price (CP) of 5112 articles = $71

And, the Sale Price (SP) of 5112 articles = $72

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)

= 72 – 71 = 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}/₇₁

= ¹⁰⁰/₇₁ = 1.41

Thus, profit = 1.41% Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 41% by selling an article for $4725.90

(2) Find the cost price, if a share broker gets a loss of 28% by selling 300 shares for $3895.20.

(3) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

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

(5) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718

(6) Calculate the earnings in percent if a vendor buys 72 coins for $1 and sells 71 coins for $1.

(7) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(8) After selling a furniture for $481.60 a shopkeeper gets a loss of 14%. In order to get a profit of 13% he should sell in for how much?

(9) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

(10) How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?