Profit And Loss
Math MCQs

Question :    If a vendor bought 21 apples per $1 and sold them at a rate of 20 apples per $1, then what would his profit percent be?

Correct Answer  5%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 21 articles = $1

The Sale Price (SP) for 20 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 21 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₁

∵ The Sale Price (SP) for 20 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₀

Calculation of profit

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

= ¹/₂₀ – ¹/₂₁

= ^{21 – 20}/₄₂₀

⇒ Profit = ¹/₄₂₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₁, the the profit = ¹/₄₂₀

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

= ^1/₄₂₀/_¹/21

= ¹/₄₂₀ × ²¹/₁

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

= ¹/₄₂₀ × ²¹/₁ × 100

= ^{1 × 21 × 100}/_{420 × 1}

= ²¹⁰⁰/₄₂₀ = 5

Thus, Profit = 5% 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 21 articles = $1

And, the Sale Price (SP) of 20 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 21 and 20 = 420

Now, Let total number of articles purchased = 420

Here, since the Cost Price of 21 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₁

Therefore, the Cost Price of 420 articles

And, since the Sale Price of 20 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₀

Therefore, the Sale Price of 420 articles

= ¹/₂₀ × 420 = $21

⇒ The Sale Price (SP) of 420 articles = $21

Now, the Cost Price (CP) of 420 articles = $20

And, the Sale Price (SP) of 420 articles = $21

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)

= 21 – 20 = 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}/₂₀

= ¹⁰⁰/₂₀ = 5

Thus, profit = 5% Answer

Similar Questions

(1) If Robert purchased a TV set in an auction at $250 and sold it at $300, then calculate the profit earned and profit percent in this sale.

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

(3) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

(4) How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

(5) The cost price of an article is $12, and the sale price is $15. Find the profit and profit percent.

(6) Noah loses 78% by selling an article for $827.20. For how much should he sell it to get a profit of 77%?

(7) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

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

(9) Calculate the earnings percentage if a hawker buys 58 articles for $1 and sells 57 articles for $1.

(10) A vendor buys 33 articles for $1 and sells 32 articles for $1. How much percent will he earn in this?