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

(1) Mr. Oliver loses 79% by selling an article for $800.10. For how much should he sell it to get a profit of 78%?

(2) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

(3) William loses 73% by selling an article for $947.70. For how much should he sell it to get a profit of 72%?

(4) Find the cost price, if a trader gets a loss of 63% by selling 15 TV sets for $4591.7

(5) Find the cost price, if a trader gets a loss of 12% by selling some of his stock of fruits for $1944.80. Find the cost price of those stock.

(6) If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

(7) After selling some articles for $22269.00 a trader earns a profit of 290%. Find the cost price.

(8) What will the earnings in percent if a vendor buys 42 apples for $1 and sells at a rate of 41 apples per $1?

(9) What will be the cost price, if a trader gets a loss of 2% by selling an article for $205.80?

(10) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?