Profit And Loss
Math MCQs

Question :    If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

Correct Answer  4.55%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 23 articles = $1

The Sale Price (SP) for 22 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 23 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₃

∵ The Sale Price (SP) for 22 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₂

Calculation of profit

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

= ¹/₂₂ – ¹/₂₃

= ^{23 – 22}/₅₀₆

⇒ Profit = ¹/₅₀₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₃, the the profit = ¹/₅₀₆

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

= ^1/₅₀₆/_¹/23

= ¹/₅₀₆ × ²³/₁

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

= ¹/₅₀₆ × ²³/₁ × 100

= ^{1 × 23 × 100}/_{506 × 1}

= ²³⁰⁰/₅₀₆ = 4.55

Thus, Profit = 4.55% 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 23 articles = $1

And, the Sale Price (SP) of 22 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 23 and 22 = 506

Now, Let total number of articles purchased = 506

Here, since the Cost Price of 23 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₃

Therefore, the Cost Price of 506 articles

And, since the Sale Price of 22 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₂

Therefore, the Sale Price of 506 articles

= ¹/₂₂ × 506 = $23

⇒ The Sale Price (SP) of 506 articles = $23

Now, the Cost Price (CP) of 506 articles = $22

And, the Sale Price (SP) of 506 articles = $23

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)

= 23 – 22 = 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}/₂₂

= ¹⁰⁰/₂₂ = 4.55

Thus, profit = 4.55% Answer

Similar Questions

(1) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(2) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(3) Mr. Donald loses 86% by selling an article for $582.40. For how much should he sell it to get a profit of 85%?

(4) 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?

(5) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(6) Mr. Bobby earns a profit of 120% by selling a TV set for $5082. What was the cost price of the TV set?

(7) In an exhibition, a trader earns a profit of 75%. His total sale was $2467.50. Find the cost price.

(8) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?

(9) A trader loses 53% by selling an article for $1179.70. For how much should he sell it to get a profit of 52%?

(10) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90