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) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

(2) If a book seller gets a loss of 33% by selling 300 books for $4294.70 then find the cost price of the books.

(3) A broker earns a profit of 310% by selling a house for $25051. Find the cost price.

(4) Find the cost price, if a trader gets a loss of 62% by selling 10 TV sets for $4639.80

(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) Find the cost price if Mr. Rocky earns a profit of 105% by selling an article for $4120.50

(7) If a broker gets a loss of 23% by selling 200 shares he had for $3395.70 then find the cost price of those shares.

(8) Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

(9) A trader loses 49% by selling an article for $1178.10. For how much should he sell it to get a profit of 48%?

(10) Mr. Bose loses 98% by selling an article for $95.20. For how much should he sell it to get a profit of 97%?