Profit And Loss
Math MCQs

Question :    Calculate the earnings percentage if a hawker buys 58 articles for $1 and sells 57 articles for $1.

Correct Answer  1.75%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 58 articles = $1

The Sale Price (SP) for 57 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 58 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₅₈

∵ The Sale Price (SP) for 57 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₅₇

Calculation of profit

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

= ¹/₅₇ – ¹/₅₈

= ^{58 – 57}/₃₃₀₆

⇒ Profit = ¹/₃₃₀₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₅₈, the the profit = ¹/₃₃₀₆

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

= ^{1/₃₃₀₆}/_¹/58

= ¹/₃₃₀₆ × ⁵⁸/₁

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

= ¹/₃₃₀₆ × ⁵⁸/₁ × 100

= ^{1 × 58 × 100}/_{3306 × 1}

= ⁵⁸⁰⁰/₃₃₀₆ = 1.75

Thus, Profit = 1.75% 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 58 articles = $1

And, the Sale Price (SP) of 57 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 58 and 57 = 3306

Now, Let total number of articles purchased = 3306

Here, since the Cost Price of 58 articles = $1

∴ the Cost Price of 1 articles = ¹/₅₈

Therefore, the Cost Price of 3306 articles

And, since the Sale Price of 57 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₅₇

Therefore, the Sale Price of 3306 articles

= ¹/₅₇ × 3306 = $58

⇒ The Sale Price (SP) of 3306 articles = $58

Now, the Cost Price (CP) of 3306 articles = $57

And, the Sale Price (SP) of 3306 articles = $58

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)

= 58 – 57 = 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}/₅₇

= ¹⁰⁰/₅₇ = 1.75

Thus, profit = 1.75% Answer

Similar Questions

(1) Find the cost price, if a trader gets a loss of 40% by selling 1000 packets of fruits for $4686

(2) Noah loses 77% by selling an article for $853.30. For how much should he sell it to get a profit of 76%?

(3) What is the cost price if a trader earns a profit of 155% by selling an article for $7675.50

(4) If a vendor buys 14 chocolates for $1 and sells 13 chocolates for $1 then, what is his profit percent?

(5) Find the profit in percent if a vendor buys 65 articles for $1 and sells 64 articles for $1.

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

(7) Find the cost price, if a shopkeeper earns a profit of 80% by selling an article for $2718

(8) A hawker buys 10 articles for $1 and sells 9 articles for $1 then, find the profit percent.

(9) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(10) Find the cost price, if a trader gets a loss of 73% by selling 100 bags of apples for $3890.70 then find the cost price of the apples.