Profit And Loss
Math MCQs

Question :    Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.

Correct Answer  3.7%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 28 articles = $1

The Sale Price (SP) for 27 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 28 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₈

∵ The Sale Price (SP) for 27 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₇

Calculation of profit

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

= ¹/₂₇ – ¹/₂₈

= ^{28 – 27}/₇₅₆

⇒ Profit = ¹/₇₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₈, the the profit = ¹/₇₅₆

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

= ^1/₇₅₆/_¹/28

= ¹/₇₅₆ × ²⁸/₁

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

= ¹/₇₅₆ × ²⁸/₁ × 100

= ^{1 × 28 × 100}/_{756 × 1}

= ²⁸⁰⁰/₇₅₆ = 3.7

Thus, Profit = 3.7% 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 28 articles = $1

And, the Sale Price (SP) of 27 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 28 and 27 = 756

Now, Let total number of articles purchased = 756

Here, since the Cost Price of 28 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₈

Therefore, the Cost Price of 756 articles

And, since the Sale Price of 27 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₇

Therefore, the Sale Price of 756 articles

= ¹/₂₇ × 756 = $28

⇒ The Sale Price (SP) of 756 articles = $28

Now, the Cost Price (CP) of 756 articles = $27

And, the Sale Price (SP) of 756 articles = $28

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)

= 28 – 27 = 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}/₂₇

= ¹⁰⁰/₂₇ = 3.7

Thus, profit = 3.7% Answer

Similar Questions

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

(3) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(4) A dealer loses 58% by selling an article for $1159.20. For how much should he sell it to get a profit of 57%?

(5) If a trader gets a loss of 20% by selling some apples for $3048, then find the cost price of those apples.

(6) If a vendor gets a loss of 70% by selling ten bags of banana for $4143 then find the cost price of all those bananas.

(7) A trader earns a profit of 170% by selling an article for $8937. Find the cost price.

(8) Find the cost price of the plot, if a dealer earns a profit of 185% by selling the plot for $10288.5

(9) Find the cost price, if a dealer earns a profit of 380% by selling an article for $36048

(10) John loses 62% by selling an article for $1124.80. For how much should he sell it to get a profit of 61%?