Profit And Loss
Math MCQs

Question :    Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??

Correct Answer  4%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 26 articles = $1

The Sale Price (SP) for 25 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 26 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₂₆

∵ The Sale Price (SP) for 25 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₂₅

Calculation of profit

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

= ¹/₂₅ – ¹/₂₆

= ^{26 – 25}/₆₅₀

⇒ Profit = ¹/₆₅₀

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₂₆, the the profit = ¹/₆₅₀

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

= ^1/₆₅₀/_¹/26

= ¹/₆₅₀ × ²⁶/₁

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

= ¹/₆₅₀ × ²⁶/₁ × 100

= ^{1 × 26 × 100}/_{650 × 1}

= ²⁶⁰⁰/₆₅₀ = 4

Thus, Profit = 4% 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 26 articles = $1

And, the Sale Price (SP) of 25 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 26 and 25 = 650

Now, Let total number of articles purchased = 650

Here, since the Cost Price of 26 articles = $1

∴ the Cost Price of 1 articles = ¹/₂₆

Therefore, the Cost Price of 650 articles

And, since the Sale Price of 25 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₂₅

Therefore, the Sale Price of 650 articles

= ¹/₂₅ × 650 = $26

⇒ The Sale Price (SP) of 650 articles = $26

Now, the Cost Price (CP) of 650 articles = $25

And, the Sale Price (SP) of 650 articles = $26

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)

= 26 – 25 = 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}/₂₅

= ¹⁰⁰/₂₅ = 4

Thus, profit = 4% Answer

Similar Questions

(1) A shopkeeper earns 130% after selling some old bikes for $5773. What was his cost price?

(2) After selling some articles for $13261.50, a trader earns a profit of 215%. Find the cost price.

(3) Mr. Robert sold his motorcycle for $1629 and got a loss of 10%. What was his cost price?

(4) If after selling 5 bags of rice for $1297.20 a shopkeeper gets a loss of 8% then what was the cost price of the rice?

(5) 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?

(6) A shopkeeper earns a profit of 175% by selling some antique articles for $9377.50. What was the cost price of those antique articles?

(7) 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.

(8) Mr. Donald loses 85% by selling an article for $616.50. For how much should he sell it to get a profit of 84%?

(9) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.

(10) Mr. Steven loses 95% by selling an article for $230.50. For how much should he sell it to get a profit of 94%?