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) Mr. Jack gets a profit of 195% by selling some articles for $11239.50. What was his cost price?

(2) Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

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

(4) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?

(5) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

(6) Jack sold a TV set at $1584. If he purchased it at $1800, then calculate his loss and loss percent in this sale.

(7) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(8) If Mr. Peter buys 17 apples for $1 and sells 16 apples for $1 then, find the profit percent in this sale.

(9) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

(10) Mr. Steven loses 96% by selling an article for $186.40. For how much should he sell it to get a profit of 95%?