Profit And Loss
Math MCQs

Question :    If Boby buys 69 pencils for $1 and sells them at a rate of 68 per $1 then, find the earnings in percentage.

Correct Answer  1.47%

Solution & Explanation

Solution

Given,

The Cost Price (CP) for 69 articles = $1

The Sale Price (SP) for 68 articles = $1

Thus, Profit percent = ?

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

∵ The Cost Price (CP) for 69 articles = $1

Therefore, the Cost Price (CP) for 1 lemon = ¹/₆₉

∵ The Sale Price (SP) for 68 articles = $1

Therefore, the Sale Price (SP) for 1 lemon = ¹/₆₈

Calculation of profit

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

= ¹/₆₈ – ¹/₆₉

= ^{69 – 68}/₄₆₉₂

⇒ Profit = ¹/₄₆₉₂

Calculation of Profit Percent using Unitary Method

∵ When the Cost Price (CP) is ¹/₆₉, the the profit = ¹/₄₆₉₂

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

= ^{1/₄₆₉₂}/_¹/69

= ¹/₄₆₉₂ × ⁶⁹/₁

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

= ¹/₄₆₉₂ × ⁶⁹/₁ × 100

= ^{1 × 69 × 100}/_{4692 × 1}

= ⁶⁹⁰⁰/₄₆₉₂ = 1.47

Thus, Profit = 1.47% 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 69 articles = $1

And, the Sale Price (SP) of 68 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 69 and 68 = 4692

Now, Let total number of articles purchased = 4692

Here, since the Cost Price of 69 articles = $1

∴ the Cost Price of 1 articles = ¹/₆₉

Therefore, the Cost Price of 4692 articles

And, since the Sale Price of 68 articles = $1

∴ The Sale Price (SP) of 1 article = ¹/₆₈

Therefore, the Sale Price of 4692 articles

= ¹/₆₈ × 4692 = $69

⇒ The Sale Price (SP) of 4692 articles = $69

Now, the Cost Price (CP) of 4692 articles = $68

And, the Sale Price (SP) of 4692 articles = $69

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)

= 69 – 68 = 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}/₆₈

= ¹⁰⁰/₆₈ = 1.47

Thus, profit = 1.47% Answer

Similar Questions

(1) A share broker earns a profit of 400% by selling his shares for $39550. For how much had he purchased those shares?

(2) If Mr. Steve buys 41 articles for $1 and sells 40 articles for $1 then find the profit percent.

(3) What was the cost price, if a trader earns a profit of 340% by selling a plot for $29524.00?

(4) How much Mr. Gates had to pay to purchase his motorbike? If he gets a profit of 70% after selling it for $2227.

(5) Calculate the earnings percentage if a vendor buys 57 articles for $1 and sells 56 articles for $1.

(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) If a trader gets a loss of 72% by selling 15 bags of apples for $3978.80 then find the cost price of the apples.

(8) Find the cost price, if a vendor gets a loss of 34% by selling some articles for $4362.60

(9) If Noah buys 32 articles for $1 and sells them at a rate of 31 articles per $1 then, find his profit percent.

(10) William loses 70% by selling an article for $1008.00 For how much should he sell it to get a profit of 69%?