Profit And Loss
Math MCQs

Question :    What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

Correct Answer  1.59%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 64 articles = $1

The Sale Price (SP) for 63 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 64 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₄

∵ The Sale Price (SP) for 63 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₃

Calculation of profit

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

= ¹/₆₃ – ¹/₆₄

= ^{64 – 63}/₄₀₃₂

⇒ Profit = ¹/₄₀₃₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₄, the the profit = ¹/₄₀₃₂

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

= ^{1/₄₀₃₂}/_¹/64

= ¹/₄₀₃₂ × ⁶⁴/₁

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

= ¹/₄₀₃₂ × ⁶⁴/₁ × 100

= ^{1 × 64 × 100}/_{4032 × 1}

= ⁶⁴⁰⁰/₄₀₃₂ = 1.59

Thus, Profit = 1.59% 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 64 articles = $1

And, the Sale Price (SP) of 63 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 64 and 63 = 4032

Now, Let total number of articles purchased = 4032

Here, since the Cost Price of 64 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₄

Therefore, the Cost Price of 4032 articles

And, since the Sale Price of 63 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₃

Therefore, the Sale Price of 4032 articles

= ¹/₆₃ × 4032 = $64

⇒ The Sale Price (SP) of 4032 articles = $64

Now, the Cost Price (CP) of 4032 articles = $63

And, the Sale Price (SP) of 4032 articles = $64

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)

= 64 – 63 = 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}/₆₃

= ¹⁰⁰/₆₃ = 1.59

Thus, profit = 1.59% Answer

Similar Questions

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(3) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

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

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

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(7) Find the cost price, if a trader gets a loss of 62% by selling 10 TV sets for $4639.80

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

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

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