Profit And Loss
Math MCQs

Question :    Calculate the earnings in percent if Mr. Peter buys 66 articles for $1 and sells 65 articles for $1.

Correct Answer  1.54%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 66 articles = $1

The Sale Price (SP) for 65 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 66 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₆

∵ The Sale Price (SP) for 65 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₅

Calculation of profit

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

= ¹/₆₅ – ¹/₆₆

= ^{66 – 65}/₄₂₉₀

⇒ Profit = ¹/₄₂₉₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₆, the the profit = ¹/₄₂₉₀

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

= ^{1/₄₂₉₀}/_¹/66

= ¹/₄₂₉₀ × ⁶⁶/₁

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

= ¹/₄₂₉₀ × ⁶⁶/₁ × 100

= ^{1 × 66 × 100}/_{4290 × 1}

= ⁶⁶⁰⁰/₄₂₉₀ = 1.54

Thus, Profit = 1.54% 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 66 articles = $1

And, the Sale Price (SP) of 65 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 66 and 65 = 4290

Now, Let total number of articles purchased = 4290

Here, since the Cost Price of 66 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₆

Therefore, the Cost Price of 4290 articles

And, since the Sale Price of 65 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₅

Therefore, the Sale Price of 4290 articles

= ¹/₆₅ × 4290 = $66

⇒ The Sale Price (SP) of 4290 articles = $66

Now, the Cost Price (CP) of 4290 articles = $65

And, the Sale Price (SP) of 4290 articles = $66

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)

= 66 – 65 = 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}/₆₅

= ¹⁰⁰/₆₅ = 1.54

Thus, profit = 1.54% Answer

Similar Questions

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(2) James loses 68% by selling an article for $1043.20. For how much should he sell it to get a profit of 67%?

(3) Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??

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(7) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(8) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(9) Find the cost price, if Mrs. Julie earns a profit of 360% by selling some articles for $32706

(10) What will be profit percent if John buys 6 articles for $1 and sells 5 articles for $1?