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) How much percent will John get if he buys 38 articles for $1 and sells 37 articles for $1?

(2) A trader loses 55% by selling an article for $1174.50. For how much should he sell it to get a profit of 54%?

(3) What will be profit percent if John buys 6 articles for $1 and sells 5 articles for $1?

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

(5) A trader earns a profit of 95% by selling an article for $3529.50. What was his cost price?

(6) If a peddler bought 71 paper clips for $1 and sold 70 paper clips for $1 then, find the profit in percent.

(7) Find the cost price, if a trader gets a loss of 35% by selling some articles for $4426.50

(8) A dealer loses 21% by selling an article for $718.90. For how much should he sell it to get a profit of 20%?

(9) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?

(10) Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??