Profit And Loss
Math MCQs

Question :    Mr. Bob buys 40 articles for $1 and sells 39 articles for $1. Find the profit percent in this sale.

Correct Answer  2.56%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 40 articles = $1

The Sale Price (SP) for 39 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 40 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₄₀

∵ The Sale Price (SP) for 39 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₉

Calculation of profit

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

= ¹/₃₉ – ¹/₄₀

= ^{40 – 39}/₁₅₆₀

⇒ Profit = ¹/₁₅₆₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₄₀, the the profit = ¹/₁₅₆₀

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

= ^{1/₁₅₆₀}/_¹/40

= ¹/₁₅₆₀ × ⁴⁰/₁

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

= ¹/₁₅₆₀ × ⁴⁰/₁ × 100

= ^{1 × 40 × 100}/_{1560 × 1}

= ⁴⁰⁰⁰/₁₅₆₀ = 2.56

Thus, Profit = 2.56% 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 40 articles = $1

And, the Sale Price (SP) of 39 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 40 and 39 = 1560

Now, Let total number of articles purchased = 1560

Here, since the Cost Price of 40 articles = $1

∴ the Cost Price of 1 articles = ¹/₄₀

Therefore, the Cost Price of 1560 articles

And, since the Sale Price of 39 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₉

Therefore, the Sale Price of 1560 articles

= ¹/₃₉ × 1560 = $40

⇒ The Sale Price (SP) of 1560 articles = $40

Now, the Cost Price (CP) of 1560 articles = $39

And, the Sale Price (SP) of 1560 articles = $40

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)

= 40 – 39 = 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}/₃₉

= ¹⁰⁰/₃₉ = 2.56

Thus, profit = 2.56% Answer

Similar Questions

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(3) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70

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(7) By selling a car for $4751.5 Mr. Aron earns a profit of 115%. For how much was he purchased his car?

(8) John purchased a bicycle in an auction at $80 and sold it at $104. Calculate the profit and profit percent in this sale.

(9) By selling a house for $14332.50, a dealer earns a profit of 225%. Find the cost price

(10) Mr. Donald loses 88% by selling an article for $511.20. For how much should he sell it to get a profit of 87%?