Profit And Loss
Math MCQs

Question :    Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.

Correct Answer  1.56%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 65 articles = $1

The Sale Price (SP) for 64 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 65 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₅

∵ The Sale Price (SP) for 64 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₄

Calculation of profit

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

= ¹/₆₄ – ¹/₆₅

= ^{65 – 64}/₄₁₆₀

⇒ Profit = ¹/₄₁₆₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₅, the the profit = ¹/₄₁₆₀

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

= ^{1/₄₁₆₀}/_¹/65

= ¹/₄₁₆₀ × ⁶⁵/₁

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

= ¹/₄₁₆₀ × ⁶⁵/₁ × 100

= ^{1 × 65 × 100}/_{4160 × 1}

= ⁶⁵⁰⁰/₄₁₆₀ = 1.56

Thus, Profit = 1.56% 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 65 articles = $1

And, the Sale Price (SP) of 64 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 65 and 64 = 4160

Now, Let total number of articles purchased = 4160

Here, since the Cost Price of 65 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₅

Therefore, the Cost Price of 4160 articles

And, since the Sale Price of 64 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₄

Therefore, the Sale Price of 4160 articles

= ¹/₆₄ × 4160 = $65

⇒ The Sale Price (SP) of 4160 articles = $65

Now, the Cost Price (CP) of 4160 articles = $64

And, the Sale Price (SP) of 4160 articles = $65

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)

= 65 – 64 = 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}/₆₄

= ¹⁰⁰/₆₄ = 1.56

Thus, profit = 1.56% Answer

Similar Questions

(1) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

(2) If a hawker buys 75 refill for $1 and sold them at a rate of 74 per $1 then calculate his profit in percentage.

(3) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

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

(5) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?

(6) By selling some goods for $3249 a shopkeeper earns a profit of 90%. Find the cost price of those goods.

(7) For how much should he sell the bicycle to get a profit of 19%, if a shopkeeper loses 20% by selling it for $688?

(8) If a hawker bought 63 candies for $1 and sold them at a rate of 62 candies per $1 then, find the profit percent.

(9) Mr. Peter buys 48 articles for $1 and sells 47 articles for $1. Find the profit percent.

(10) Mr. John buys 28 articles for $1 and sells 27 articles for $1 then, find his profit percent.