Profit And Loss
Math MCQs

Question :    Find the earnings percentage if a peddler buys 51 articles for $1 and sells 50 articles for $1.

Correct Answer  2%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 51 articles = $1

The Sale Price (SP) for 50 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 51 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₁

∵ The Sale Price (SP) for 50 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₀

Calculation of profit

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

= ¹/₅₀ – ¹/₅₁

= ^{51 – 50}/₂₅₅₀

⇒ Profit = ¹/₂₅₅₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₁, the the profit = ¹/₂₅₅₀

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

= ^{1/₂₅₅₀}/_¹/51

= ¹/₂₅₅₀ × ⁵¹/₁

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

= ¹/₂₅₅₀ × ⁵¹/₁ × 100

= ^{1 × 51 × 100}/_{2550 × 1}

= ⁵¹⁰⁰/₂₅₅₀ = 2

Thus, Profit = 2% 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 51 articles = $1

And, the Sale Price (SP) of 50 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 51 and 50 = 2550

Now, Let total number of articles purchased = 2550

Here, since the Cost Price of 51 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₁

Therefore, the Cost Price of 2550 articles

And, since the Sale Price of 50 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₀

Therefore, the Sale Price of 2550 articles

= ¹/₅₀ × 2550 = $51

⇒ The Sale Price (SP) of 2550 articles = $51

Now, the Cost Price (CP) of 2550 articles = $50

And, the Sale Price (SP) of 2550 articles = $51

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)

= 51 – 50 = 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}/₅₀

= ¹⁰⁰/₅₀ = 2

Thus, profit = 2% Answer

Similar Questions

(1) John purchased a bike for $500 and he sold it at a gain of 12%. Find the sale price of the bike.

(2) Find the cost price, if a dealer gets a loss of 32% by selling 500 books for $4222.80.

(3) A shopkeeper loses 27% by selling some articles for $883.30. For how much should he sell them to get a profit of 26%?

(4) Find the cost price, if a trader earns a profit of 5% by selling an article for $10.5

(5) In an auction, Mr. Jojo got $27242.5 for his antique bike. If he got a profit of 325% in this deal, then what was his cost price.?

(6) If a vendor bought 20 apples per $1 and sold them at a rate of 19 apples per $1, then what would his profit percent be?

(7) How much percent will John get if he buys 39 articles for $1 and sells at a rate of 38 articles per $1?

(8) Mr. Robert buys 31 articles for $1 and sells 30 articles for $1. Find the profit in percent.

(9) Mrs. Mary loses 19% by selling an article for $656.10. For how much should she sell it to get a profit of 18%?

(10) Calculate the cost price, if a trader gets a loss of 3% by selling an article for $397.70