Profit And Loss
Math MCQs

Question :    How much percent will a hawker earn, if he buys 34 articles for $1 and sells 33 articles for $1?

Correct Answer  3.03%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 34 articles = $1

The Sale Price (SP) for 33 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 34 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₃₄

∵ The Sale Price (SP) for 33 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₃₃

Calculation of profit

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

= ¹/₃₃ – ¹/₃₄

= ^{34 – 33}/₁₁₂₂

⇒ Profit = ¹/₁₁₂₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₃₄, the the profit = ¹/₁₁₂₂

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

= ^{1/₁₁₂₂}/_¹/34

= ¹/₁₁₂₂ × ³⁴/₁

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

= ¹/₁₁₂₂ × ³⁴/₁ × 100

= ^{1 × 34 × 100}/_{1122 × 1}

= ³⁴⁰⁰/₁₁₂₂ = 3.03

Thus, Profit = 3.03% 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 34 articles = $1

And, the Sale Price (SP) of 33 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 34 and 33 = 1122

Now, Let total number of articles purchased = 1122

Here, since the Cost Price of 34 articles = $1

∴ the Cost Price of 1 articles = ¹/₃₄

Therefore, the Cost Price of 1122 articles

And, since the Sale Price of 33 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₃₃

Therefore, the Sale Price of 1122 articles

= ¹/₃₃ × 1122 = $34

⇒ The Sale Price (SP) of 1122 articles = $34

Now, the Cost Price (CP) of 1122 articles = $33

And, the Sale Price (SP) of 1122 articles = $34

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)

= 34 – 33 = 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}/₃₃

= ¹⁰⁰/₃₃ = 3.03

Thus, profit = 3.03% Answer

Similar Questions

(1) A dealer sold a plot for $26502.00. In this deal, if the dealer earns a profit of 320%, then find the cost price.

(2) Mr. Steven loses 92% by selling an article for $356.80. For how much should he sell it to get a profit of 91%?

(3) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

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

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

(6) Find the cost price, if by selling some articles for $13792 a trader earns a profit of 220%

(7) For how much should Mr. John sell it to get a profit of 3% if he loses 4% by selling an article for $57.60?

(8) Find the cost price, if a trader gets a loss of 68% by selling five bags of rice for $4291.20

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

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