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) Mrs. Mary earns a profit of 230% after selling an article for $14883. Find the cost price.

(2) If a dealer earns a profit of 260% by selling an article for $18396.00. Find the cost price.

(3) For how much Mr. Peter should sell his books to get a profit of 11%? If he loses 12% by selling them for $404.80.

(4) Find the cost price, if Mrs. Olivia earns a profit of 160% by selling some articles for $8086

(5) Find the cost price, if a trader gets a loss of 51% by selling 200 bags of rice for $4904.90

(6) If a hawker buys buys 61 oranges for $1 and sells them at a rate of 60 oranges per $1 then, find the profit percent.

(7) A dealer loses 56% by selling an article for $1170.40. For how much should he sell it to get a profit of 55%?

(8) Find the cost price, if Mr. Oliver earns a profit of 150% by selling an article for $7275.00

(9) By selling an article for $1125.30 a vendor gets a loss of 7%. Calculate the cost price.

(10) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.