Profit And Loss
Math MCQs

Question :    If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

Correct Answer  2.22%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 46 articles = $1

The Sale Price (SP) for 45 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 46 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₆

∵ The Sale Price (SP) for 45 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₄₅

Calculation of profit

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

= ¹/₄₅ – ¹/₄₆

= ^{46 – 45}/₂₀₇₀

⇒ Profit = ¹/₂₀₇₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₆, the the profit = ¹/₂₀₇₀

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

= ^{1/₂₀₇₀}/_¹/46

= ¹/₂₀₇₀ × ⁴⁶/₁

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

= ¹/₂₀₇₀ × ⁴⁶/₁ × 100

= ^{1 × 46 × 100}/_{2070 × 1}

= ⁴⁶⁰⁰/₂₀₇₀ = 2.22

Thus, Profit = 2.22% 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 46 articles = $1

And, the Sale Price (SP) of 45 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 46 and 45 = 2070

Now, Let total number of articles purchased = 2070

Here, since the Cost Price of 46 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₆

Therefore, the Cost Price of 2070 articles

And, since the Sale Price of 45 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₄₅

Therefore, the Sale Price of 2070 articles

= ¹/₄₅ × 2070 = $46

⇒ The Sale Price (SP) of 2070 articles = $46

Now, the Cost Price (CP) of 2070 articles = $45

And, the Sale Price (SP) of 2070 articles = $46

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)

= 46 – 45 = 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}/₄₅

= ¹⁰⁰/₄₅ = 2.22

Thus, profit = 2.22% Answer

Similar Questions

(1) The cost price of an article is $15 and the sale price is $20, then find the profit and profit percent.

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

(3) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?

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

(6) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

(7) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(8) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.

(9) Find the cost price, if a trader gets a loss of 69% by selling 12 bags of fruit for $4219.10

(10) A pddler buys 47 candies for $1 and sells at a rate of 46 candies per $1 then find the profit percent.