Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

Correct Answer  1.96%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 52 articles = $1

The Sale Price (SP) for 51 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 52 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₂

∵ The Sale Price (SP) for 51 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₁

Calculation of profit

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

= ¹/₅₁ – ¹/₅₂

= ^{52 – 51}/₂₆₅₂

⇒ Profit = ¹/₂₆₅₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₂, the the profit = ¹/₂₆₅₂

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

= ^{1/₂₆₅₂}/_¹/52

= ¹/₂₆₅₂ × ⁵²/₁

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

= ¹/₂₆₅₂ × ⁵²/₁ × 100

= ^{1 × 52 × 100}/_{2652 × 1}

= ⁵²⁰⁰/₂₆₅₂ = 1.96

Thus, Profit = 1.96% 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 52 articles = $1

And, the Sale Price (SP) of 51 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 52 and 51 = 2652

Now, Let total number of articles purchased = 2652

Here, since the Cost Price of 52 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₂

Therefore, the Cost Price of 2652 articles

And, since the Sale Price of 51 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₁

Therefore, the Sale Price of 2652 articles

= ¹/₅₁ × 2652 = $52

⇒ The Sale Price (SP) of 2652 articles = $52

Now, the Cost Price (CP) of 2652 articles = $51

And, the Sale Price (SP) of 2652 articles = $52

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)

= 52 – 51 = 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}/₅₁

= ¹⁰⁰/₅₁ = 1.96

Thus, profit = 1.96% Answer

Similar Questions

(1) William loses 43% by selling an article for $1145.70. For how much should he sell it to get a profit of 42%?

(2) Mr. Oliver loses 83% by selling an article for $681.70. For how much should he sell it to get a profit of 82%?

(3) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(4) Mr. John earns a profit of 190% by selling a old car for $10759. For how much had he purchased that house?

(5) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(6) A trader loses 47% by selling an article for $1171.30. For how much should he sell it to get a profit of 46%?

(7) 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.

(8) What will be the cost price if Peter eans a profit of 15% by selling a scooty for $241.5?

(9) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(10) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.