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) A dealer sold an antique piece of a car $25771.50. If he earns a profit of 315%, then find his cost price.

(2) By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

(3) Mr. Bose loses 97% by selling an article for $141.30. For how much should he sell it to get a profit of 96%?

(4) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?

(5) Mrs. John earned a profit of 330% by selling her car. If she sold her car for $27993, then find the cost price of the car.

(6) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(7) On a closing day, a shopkeeper earns a profit of 65%. If gets $1996.5 in total, then what was his cost price?

(8) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90

(9) A trader gets a loss of 52% by selling 500 bags of rice for $4900.80. Find the cost price of rice.

(10) Mr. Steven loses 94% by selling an article for $273.60. For how much should he sell it to get a profit of 93%?