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) If a vendor buys 7 lemons for $1 and sells 6 lemons for $1 then, what is the profit percent in this sale?

(2) Potter loses 89% by selling an article for $474.10. For how much should he sell it to get a profit of 88%?

(3) Mollie purchased 150 kg of wheat at $1350. Due to some unavoidable circumstances, he had to sell the wheat at $7.20 per kg. Calculate his total loss and loss percent in this sale.

(4) In a deal, Mr. Kart earns a profit of 85%. He got a total of $2978.50 in the deal. What was the cost price of this deal?

(5) If a vendor bought 62 candies for $1 and sold 61 candies per $1 then find the profit percent.

(6) Find the cost price, if a trader gets a loss of 58% by selling two TV sets for $4792.20

(7) A dealer loses 59% by selling an article for $1152.10. For how much should he sell it to get a profit of 58%?

(8) If a hawker bought 23 apples per $1 and sold them at a rate of 22 apples per $1, then what would his profit percent be?

(9) What is the cost price; if a trader earns a profit of 295% by selling some articles for $22949.50?

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