Profit And Loss
Math MCQs

Question :    Mrs. Julie purchased 27 oranges for $1 and sold 26 oranges for $1. What will be his profit percentage?

Correct Answer  3.85%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 27 articles = $1

The Sale Price (SP) for 26 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 27 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₇

∵ The Sale Price (SP) for 26 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₆

Calculation of profit

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

= ¹/₂₆ – ¹/₂₇

= ^{27 – 26}/₇₀₂

⇒ Profit = ¹/₇₀₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₇, the the profit = ¹/₇₀₂

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

= ^1/₇₀₂/_¹/27

= ¹/₇₀₂ × ²⁷/₁

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

= ¹/₇₀₂ × ²⁷/₁ × 100

= ^{1 × 27 × 100}/_{702 × 1}

= ²⁷⁰⁰/₇₀₂ = 3.85

Thus, Profit = 3.85% 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 27 articles = $1

And, the Sale Price (SP) of 26 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 27 and 26 = 702

Now, Let total number of articles purchased = 702

Here, since the Cost Price of 27 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₇

Therefore, the Cost Price of 702 articles

And, since the Sale Price of 26 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₆

Therefore, the Sale Price of 702 articles

= ¹/₂₆ × 702 = $27

⇒ The Sale Price (SP) of 702 articles = $27

Now, the Cost Price (CP) of 702 articles = $26

And, the Sale Price (SP) of 702 articles = $27

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)

= 27 – 26 = 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}/₂₆

= ¹⁰⁰/₂₆ = 3.85

Thus, profit = 3.85% Answer

Similar Questions

(1) Find the earnings in percent if a vendor buys 43 articles for $1 and sells 42 articles for $1.

(2) Find the earnings percentage if a vendor buys 52 articles for $1 and sells 51 articles for $1.

(3) Find the cost price, if a share broker gets a loss of 29% by selling 500 stocks for $3983.10

(4) If a trader gets a loss of 25% by selling some shares for $3607.50, then find the cost price of those shares.

(5) Mr. Donald loses 86% by selling an article for $582.40. For how much should he sell it to get a profit of 85%?

(6) A trader loses 30% by selling an article for $952. For how much should he sell it to get a profit of 29%?

(7) Find the cost price, if a dealer earns a profit of 305% by selling a plot for $24340.50

(8) Find the cost price, if a trader gets a loss of 41% by selling an article for $4725.90

(9) Find the cost price, if a vendor gets a loss of 56% by selling a TV set for $4844.40.

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