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) A dealer loses 60% by selling an article for $1144.00. For how much should he sell it to get a profit of 59%?

(2) Mr. Henry loses 26% by selling an article for $858.4. For how much should he sell it to get a profit of 25%?

(3) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(4) For how much had Mr. Robert purchased his motorcycle if he earns a profit of 60% by selling it for $1776?

(5) Find the cost price, if a trader gets a loss of 47% by selling 500 kg rice for $4881.30

(6) Find the earnings percentage if a hawker buys 50 articles for $1 and sells 49 articles for $1.

(7) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.

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

(9) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(10) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?