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) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.

(2) Mr. Steven loses 93% by selling an article for $315.70. For how much should he sell it to get a profit of 92%?

(3) How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?

(4) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(5) 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.

(6) What will be the earnings in percent if a vendor buys 45 articles for $1 and sells 44 articles for $1?

(7) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(8) What was the cost price, if a trader gets a loss of 17% by selling an article for $2664.30?

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

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