Profit And Loss
Math MCQs

Question :    A peddler buys 11 oranges for $1 and sells 10 oranges for $1 then, find his profit percent.

Correct Answer  10%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 11 articles = $1

The Sale Price (SP) for 10 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 11 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₁₁

∵ The Sale Price (SP) for 10 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₀

Calculation of profit

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

= ¹/₁₀ – ¹/₁₁

= ^{11 – 10}/₁₁₀

⇒ Profit = ¹/₁₁₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₁₁, the the profit = ¹/₁₁₀

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

= ^1/₁₁₀/_¹/11

= ¹/₁₁₀ × ¹¹/₁

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

= ¹/₁₁₀ × ¹¹/₁ × 100

= ^{1 × 11 × 100}/_{110 × 1}

= ¹¹⁰⁰/₁₁₀ = 10

Thus, Profit = 10% 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 11 articles = $1

And, the Sale Price (SP) of 10 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 11 and 10 = 110

Now, Let total number of articles purchased = 110

Here, since the Cost Price of 11 articles = $1

∴ the Cost Price of 1 articles = ¹/₁₁

Therefore, the Cost Price of 110 articles

And, since the Sale Price of 10 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₀

Therefore, the Sale Price of 110 articles

= ¹/₁₀ × 110 = $11

⇒ The Sale Price (SP) of 110 articles = $11

Now, the Cost Price (CP) of 110 articles = $10

And, the Sale Price (SP) of 110 articles = $11

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)

= 11 – 10 = 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}/₁₀

= ¹⁰⁰/₁₀ = 10

Thus, profit = 10% Answer

Similar Questions

(1) Calculate the earnings percentage if a vendor buys 55 articles for $1 and sells 54 articles for $1.

(2) 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?

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

(4) A trader earns a profit of 100% by selling an article for $3820.00. Find the cost price.

(5) A dealer loses 28% by selling some articles for $907.20. For how much should he sell them to get a profit of 27%?

(6) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(7) Find the cost price, if a dealer earns a profit of 250% by selling a plot for $17185

(8) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(9) If a shopkeeper gets a loss of 53% by selling 200 kg of rice for $4892.70 then find the cost price of rice.

(10) A fruit seller gets a loss of 6% by selling an his old stock for $949.40. What was his cost price?