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

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(2) Find the cost price, if a dealer gets a loss of 31% by selling 400 stocks for $4146.90

(3) What will be the profit percentage if a hawker buys 64 articles for $1 and sells 63 articles for $1?

(4) If a peddler buys 46 articles for $1 and sells 45 articles for $1 then, find the earnings in percentage.

(5) A car dealer earns 135% by selling an old antique car for $6133.50. For how much had he purchased that car?

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

(7) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

(8) Find the earnings percentage if a vendor buys 53 articles for $1 and sells 52 articles for $1.

(9) What will be the earnings in percent if a hawker buys 59 articles for $1 and sells 58 articles for $1?

(10) Find the cost price, if a trader gets a loss of 69% by selling 12 bags of fruit for $4219.10