Profit And Loss
Math MCQs

Question :    What will be profit percent if John buys 6 articles for $1 and sells 5 articles for $1?

Correct Answer  20%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 6 articles = $1

The Sale Price (SP) for 5 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 6 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆

∵ The Sale Price (SP) for 5 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅

Calculation of profit

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

= ¹/₅ – ¹/₆

= ^{6 – 5}/₃₀

⇒ Profit = ¹/₃₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆, the the profit = ¹/₃₀

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

= ^1/₃₀/_¹/6

= ¹/₃₀ × ⁶/₁

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

= ¹/₃₀ × ⁶/₁ × 100

= ^{1 × 6 × 100}/_{30 × 1}

= ⁶⁰⁰/₃₀ = 20

Thus, Profit = 20% 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 6 articles = $1

And, the Sale Price (SP) of 5 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 6 and 5 = 30

Now, Let total number of articles purchased = 30

Here, since the Cost Price of 6 articles = $1

∴ the Cost Price of 1 articles = ¹/₆

Therefore, the Cost Price of 30 articles

And, since the Sale Price of 5 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅

Therefore, the Sale Price of 30 articles

= ¹/₅ × 30 = $6

⇒ The Sale Price (SP) of 30 articles = $6

Now, the Cost Price (CP) of 30 articles = $5

And, the Sale Price (SP) of 30 articles = $6

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)

= 6 – 5 = 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}/₅

= ¹⁰⁰/₅ = 20

Thus, profit = 20% Answer

Similar Questions

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(8) James loses 65% by selling an article for $1088.50. For how much should he sell it to get a profit of 64%?

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

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