Profit And Loss
Math MCQs

Question :    If a seller bought 24 apples per $1 and sold them at a rate of 23 apples per $1, then what would his profit percent be?

Correct Answer  4.35%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 24 articles = $1

The Sale Price (SP) for 23 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 24 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₄

∵ The Sale Price (SP) for 23 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₃

Calculation of profit

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

= ¹/₂₃ – ¹/₂₄

= ^{24 – 23}/₅₅₂

⇒ Profit = ¹/₅₅₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₄, the the profit = ¹/₅₅₂

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

= ^1/₅₅₂/_¹/24

= ¹/₅₅₂ × ²⁴/₁

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

= ¹/₅₅₂ × ²⁴/₁ × 100

= ^{1 × 24 × 100}/_{552 × 1}

= ²⁴⁰⁰/₅₅₂ = 4.35

Thus, Profit = 4.35% 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 24 articles = $1

And, the Sale Price (SP) of 23 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 24 and 23 = 552

Now, Let total number of articles purchased = 552

Here, since the Cost Price of 24 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₄

Therefore, the Cost Price of 552 articles

And, since the Sale Price of 23 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₃

Therefore, the Sale Price of 552 articles

= ¹/₂₃ × 552 = $24

⇒ The Sale Price (SP) of 552 articles = $24

Now, the Cost Price (CP) of 552 articles = $23

And, the Sale Price (SP) of 552 articles = $24

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)

= 24 – 23 = 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}/₂₃

= ¹⁰⁰/₂₃ = 4.35

Thus, profit = 4.35% Answer

Similar Questions

(1) A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent.

(2) Find the cost price, if Mrs. Olivia earns a profit of 160% by selling some articles for $8086

(3) James loses 66% by selling an article for $1074.40. For how much should he sell it to get a profit of 65%?

(4) Find the cost price, if a shopkeeper earns a profit of 300% by selling some articles for $23640

(5) Mr. Boby loses 15% by selling an article for $518.50. For how much should he sell it to get a profit of 14%?

(6) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?

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

(8) Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.

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

(10) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.