Profit And Loss
Math MCQs

Question :    How much percent will a vendor earn if he buys 36 articles for $1 and sells them at a rate of 35 articles per $1?

Correct Answer  2.86%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 36 articles = $1

The Sale Price (SP) for 35 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 36 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₆

∵ The Sale Price (SP) for 35 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₅

Calculation of profit

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

= ¹/₃₅ – ¹/₃₆

= ^{36 – 35}/₁₂₆₀

⇒ Profit = ¹/₁₂₆₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₆, the the profit = ¹/₁₂₆₀

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

= ^{1/₁₂₆₀}/_¹/36

= ¹/₁₂₆₀ × ³⁶/₁

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

= ¹/₁₂₆₀ × ³⁶/₁ × 100

= ^{1 × 36 × 100}/_{1260 × 1}

= ³⁶⁰⁰/₁₂₆₀ = 2.86

Thus, Profit = 2.86% 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 36 articles = $1

And, the Sale Price (SP) of 35 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 36 and 35 = 1260

Now, Let total number of articles purchased = 1260

Here, since the Cost Price of 36 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₆

Therefore, the Cost Price of 1260 articles

And, since the Sale Price of 35 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₅

Therefore, the Sale Price of 1260 articles

= ¹/₃₅ × 1260 = $36

⇒ The Sale Price (SP) of 1260 articles = $36

Now, the Cost Price (CP) of 1260 articles = $35

And, the Sale Price (SP) of 1260 articles = $36

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)

= 36 – 35 = 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}/₃₅

= ¹⁰⁰/₃₅ = 2.86

Thus, profit = 2.86% Answer

Similar Questions

(1) A shopkeeper gets a loss of 5% by selling some fruits for $769.50. Find the cost price of the furits.

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

(3) A shopkeeper earns a profit of 50% by selling an article for $1365. Find the cost price of the article.

(4) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(5) Mr. Peter loses 44% by selling an article for $1153.60. For how much should he sell it to get a profit of 43%?

(6) Find the cost price, if a trader gets a loss of 45% by selling 800 bags of fruits for $4845.50

(7) If a trader gets a loss of 55% by selling 15 bags of fruits for $4864.50 then find the cost price of fruits.

(8) After selling an article for $282.10, a shopkeeper gets a loss of 9%. Thus, to earn a profit of 8% he should sell it at which price?

(9) If a dealer earns a profit of 255% by selling some articles for $17785.50, then find the cost price.

(10) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718