Profit And Loss
Math MCQs

Question :    How much percent will a vendor earn, if he buys 35 articles for $1 and sells 34 articles for $1?

Correct Answer  2.94%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 35 articles = $1

The Sale Price (SP) for 34 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 35 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₅

∵ The Sale Price (SP) for 34 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₄

Calculation of profit

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

= ¹/₃₄ – ¹/₃₅

= ^{35 – 34}/₁₁₉₀

⇒ Profit = ¹/₁₁₉₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₅, the the profit = ¹/₁₁₉₀

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

= ^{1/₁₁₉₀}/_¹/35

= ¹/₁₁₉₀ × ³⁵/₁

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

= ¹/₁₁₉₀ × ³⁵/₁ × 100

= ^{1 × 35 × 100}/_{1190 × 1}

= ³⁵⁰⁰/₁₁₉₀ = 2.94

Thus, Profit = 2.94% 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 35 articles = $1

And, the Sale Price (SP) of 34 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 35 and 34 = 1190

Now, Let total number of articles purchased = 1190

Here, since the Cost Price of 35 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₅

Therefore, the Cost Price of 1190 articles

And, since the Sale Price of 34 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₄

Therefore, the Sale Price of 1190 articles

= ¹/₃₄ × 1190 = $35

⇒ The Sale Price (SP) of 1190 articles = $35

Now, the Cost Price (CP) of 1190 articles = $34

And, the Sale Price (SP) of 1190 articles = $35

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)

= 35 – 34 = 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}/₃₄

= ¹⁰⁰/₃₄ = 2.94

Thus, profit = 2.94% Answer

Similar Questions

(1) Bill sold his secondhand motorcycle for $512.50. In this sale, he got a profit of 25%. For how much amount had he purchased the motorcycle?

(2) A shopkeeper earns a profit of 125% after selling some items for $5422.50. Find the cost price of those items.

(3) Mr. Razor loses 45% by selling an article for $1160.50. For how much should he sell it to get a profit of 44%?

(4) Find the cost price, if a fruit seller gets a loss of 43% by selling 500 bags of fruits for $4793.70

(5) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?

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

(7) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?

(8) Find the cost price, if a trader gets a loss of 39% by selling 100 packets of fruits for $4642.10

(9) If a vendor purchased 73 coins for $1 and sells 72 coins for $1 then, find profit in percent.

(10) What is the cost price, if Mrs. Jill earns a profit of 200% by selling some items for $11730?