Profit And Loss
Math MCQs

Question :    If John buys 68 pencils for $1 and sells them at a rate of 67 per $1 then calculate the profit percent in this selling.

Correct Answer  1.49%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 68 articles = $1

The Sale Price (SP) for 67 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 68 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₈

∵ The Sale Price (SP) for 67 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₇

Calculation of profit

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

= ¹/₆₇ – ¹/₆₈

= ^{68 – 67}/₄₅₅₆

⇒ Profit = ¹/₄₅₅₆

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₈, the the profit = ¹/₄₅₅₆

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

= ^{1/₄₅₅₆}/_¹/68

= ¹/₄₅₅₆ × ⁶⁸/₁

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

= ¹/₄₅₅₆ × ⁶⁸/₁ × 100

= ^{1 × 68 × 100}/_{4556 × 1}

= ⁶⁸⁰⁰/₄₅₅₆ = 1.49

Thus, Profit = 1.49% 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 68 articles = $1

And, the Sale Price (SP) of 67 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 68 and 67 = 4556

Now, Let total number of articles purchased = 4556

Here, since the Cost Price of 68 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₈

Therefore, the Cost Price of 4556 articles

And, since the Sale Price of 67 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₇

Therefore, the Sale Price of 4556 articles

= ¹/₆₇ × 4556 = $68

⇒ The Sale Price (SP) of 4556 articles = $68

Now, the Cost Price (CP) of 4556 articles = $67

And, the Sale Price (SP) of 4556 articles = $68

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)

= 68 – 67 = 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}/₆₇

= ¹⁰⁰/₆₇ = 1.49

Thus, profit = 1.49% Answer

Similar Questions

(1) What was the cost price, if a trader gets a loss of 18% by selling some articles for $2796.20?

(2) Find the cost price, if a trader gets a loss of 74% by selling 50 bags of rice for $3798.60

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

(4) Mr. Oliver loses 34% by selling an article for $1029.60. For how much should he sell it to get a profit of 33%?

(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) Find the cost price, if a trader gets a loss of 54% by selling 100 bags of mobile covers for $4880.60

(7) For how much should he sell it to get a profit of 16%, if Mr. Bond loses 17% by selling a bicycle for $589.30?

(8) If a trader earned a profit of 350% by selling a housing plot for $31095 then, what was the cost price of the plot?

(9) While shifting to the other city, Mr. Bob sold all of the furniture and got a profit of 35%. If he sold them for $823.50, then for how much had he purchased them?

(10) A shopkeeper loses 46% by selling an article for $1166.40. For how much should he sell it to get a profit of 45%?