Profit And Loss
Math MCQs

Question :    If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

Correct Answer  7.69%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 14 articles = $1

The Sale Price (SP) for 13 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 14 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₁₄

∵ The Sale Price (SP) for 13 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₃

Calculation of profit

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

= ¹/₁₃ – ¹/₁₄

= ^{14 – 13}/₁₈₂

⇒ Profit = ¹/₁₈₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₁₄, the the profit = ¹/₁₈₂

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

= ^1/₁₈₂/_¹/14

= ¹/₁₈₂ × ¹⁴/₁

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

= ¹/₁₈₂ × ¹⁴/₁ × 100

= ^{1 × 14 × 100}/_{182 × 1}

= ¹⁴⁰⁰/₁₈₂ = 7.69

Thus, Profit = 7.69% 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 14 articles = $1

And, the Sale Price (SP) of 13 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 14 and 13 = 182

Now, Let total number of articles purchased = 182

Here, since the Cost Price of 14 articles = $1

∴ the Cost Price of 1 articles = ¹/₁₄

Therefore, the Cost Price of 182 articles

And, since the Sale Price of 13 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₃

Therefore, the Sale Price of 182 articles

= ¹/₁₃ × 182 = $14

⇒ The Sale Price (SP) of 182 articles = $14

Now, the Cost Price (CP) of 182 articles = $13

And, the Sale Price (SP) of 182 articles = $14

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)

= 14 – 13 = 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}/₁₃

= ¹⁰⁰/₁₃ = 7.69

Thus, profit = 7.69% Answer

Similar Questions

(1) What will be profit percent if a peddler buys 12 kiwis for $1 and sells 11 kiwis for $1?

(2) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(3) Mr. Steven loses 94% by selling an article for $273.60. For how much should he sell it to get a profit of 93%?

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

(5) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

(6) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(7) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(8) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

(9) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(10) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.