Profit And Loss
Math MCQs

Question :    Mr. Jack buys 13 articles for $1 and sells 12 articles for $1. Find his profit percent.

Correct Answer  8.33%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 13 articles = $1

The Sale Price (SP) for 12 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 13 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₁₃

∵ The Sale Price (SP) for 12 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₁₂

Calculation of profit

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

= ¹/₁₂ – ¹/₁₃

= ^{13 – 12}/₁₅₆

⇒ Profit = ¹/₁₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₁₃, the the profit = ¹/₁₅₆

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

= ^1/₁₅₆/_¹/13

= ¹/₁₅₆ × ¹³/₁

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

= ¹/₁₅₆ × ¹³/₁ × 100

= ^{1 × 13 × 100}/_{156 × 1}

= ¹³⁰⁰/₁₅₆ = 8.33

Thus, Profit = 8.33% 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 13 articles = $1

And, the Sale Price (SP) of 12 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 13 and 12 = 156

Now, Let total number of articles purchased = 156

Here, since the Cost Price of 13 articles = $1

∴ the Cost Price of 1 articles = ¹/₁₃

Therefore, the Cost Price of 156 articles

And, since the Sale Price of 12 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₁₂

Therefore, the Sale Price of 156 articles

= ¹/₁₂ × 156 = $13

⇒ The Sale Price (SP) of 156 articles = $13

Now, the Cost Price (CP) of 156 articles = $12

And, the Sale Price (SP) of 156 articles = $13

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)

= 13 – 12 = 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}/₁₂

= ¹⁰⁰/₁₂ = 8.33

Thus, profit = 8.33% Answer

Similar Questions

(1) By selling some antique items for $20938 Mr. David earns a profit of 280%. Find the cost price.

(2) John gets a 20% profit after selling his laptop for $372. What was the cost price of the laptop?

(3) A trader loses 54% by selling an article for $1177.60. For how much should he sell it to get a profit of 53%?

(4) Find the cost price, if a share broker gets a loss of 26% by selling 100 shares for $3707.40.

(5) A peddler purchased 25 apples per $1 and sold them at a rate of 24 apples per $1. What will be the profit percent?

(6) If a trader gets a loss of 16% by selling some articles for $2528.40 then find the cost price.

(7) A trader earns a profit of 170% by selling an article for $8937. Find the cost price.

(8) A shopkeeper loses 31% by selling an article for $972.90. For how much should he sell it to get a profit of 30%?

(9) By selling a bicycle for $443.70 a shopkeeper loses 13%. For how much should he sell it to get a profit of 12%?

(10) A hawker buys 19 articles for $1 and sold then at the rate of 18 articles per $1. What was this profit percent?